Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]00 (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

Question

Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]00 ​(Type an integer or a simplified fraction. Use a comma to separate answers as​ needed.)

BlackTom AI · Accepted Answer

The problem asks us to solve the quadratic equation by factoring: 63x − 36x^2 = 0.

First, factor out the greatest common factor from both terms. Both 63x and 36x^2 share x, so we can factor x: x(63 − 36x) = 0.

Now apply the zero-product property: a product is zero if and only if at least one factor is zero.

Option a: x = 0. If x = 0, the left-hand side becomes 0, satisfying the equation. So x = 0 is a valid root.

Option b: 63 − 36x = 0. Solve for x: 63 = 36x, hence x = 63/36. Reduce the fraction by the greatest common divisor 9: 63/36 = 7/4. Therefore, x = 7/4 is another root.

Thus, the equation has two roots: x = 0 and x = 7/4. The provided answers ["0", "7/4"] correspond exactly to these roots.

Notes:
- The factoring step x(63 − 36x) = 0 is a straightforward application of factoring out the common factor.
- The simplification 63/36 reduces to 7/4, confirming the second root.
- There are no extraneous solutions introduced by this method, since both steps stem directly from valid algebraic manipulations.

Homework:Module 7 Homework (Quadratics)

Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]00 (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

查看解析

登录即可查看完整答案

类似问题

Part 1Solve by using the square root property.(xminus−77)squared2equals=6464 Part 1The solution(s) is(are) x = [input]enter your response here .(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)

Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]enter your response here (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

Solve. 3 𝑥 4 = 3 𝑥 ( 56 𝑥 − 𝑥 2 ) Select ALL numbers which are solutions to this equation.

Solve the following equation by factorisation on paper: 12 𝑥 2 + 7 𝑥 − 10 = 0 AND In this quiz, enter the coefficient of the term with the highest power of x. (Answer in quiz: 1 mark) (Written answer: 2 marks)

If , which of the following gives the value(s) of ?

Solve the quadratic by factoring: If you have multiple answers, separate them with a comma. Reduce all fractions. Enter fractions using "/".

Solve the equation that is in quadratic form. (2x+5)2+21=−10(2x+5)

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单

Homework:Module 7 Homework (Quadratics)

Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]00 ​(Type an integer or a simplified fraction. Use a comma to separate answers as​ needed.)

查看解析

登录即可查看完整答案

类似问题

Part 1Solve by using the square root property.​(xminus−77​)squared2equals=6464 Part 1The​ solution(s) is(are) x​ = [input]enter your response here .​(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as​ needed.)

Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]enter your response here ​(Type an integer or a simplified fraction. Use a comma to separate answers as​ needed.)

Solve. 3 𝑥 4 = 3 𝑥 ( 56 𝑥 − 𝑥 2 ) Select ALL numbers which are solutions to this equation.

Solve the following equation by factorisation on paper: 12 𝑥 2 + 7 𝑥 − 10 = 0 AND In this quiz, enter the coefficient of the term with the highest power of x. (Answer in quiz: 1 mark) (Written answer: 2 marks)

If , which of the following gives the value(s) of ?

Solve the quadratic by factoring: If you have multiple answers, separate them with a comma. Reduce all fractions. Enter fractions using "/".

Solve the equation that is in quadratic form. (2x+5)2+21=−10(2x+5)

更多留学生实用工具

希望你的学习变得更简单

Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]00 (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

Part 1Solve by using the square root property.(xminus−77)squared2equals=6464 Part 1The solution(s) is(are) x = [input]enter your response here .(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)

Part 1Solve the given quadratic equation by factoring.63 x minus 36 x squared equals 063x−36x2=0 Part 1xequals=[input]enter your response here (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)