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.)

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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.)

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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.)

View Explanation

Log in for full answers

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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.)

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