Question

Use factoring to solve the quadratic equation. Check by substitution or by using a graphing utility and identifying x-intercepts.
2x² = 13x +7
Rewrite the equation in factored form.

Answer 1

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Answer:

  x = -1/2, x = 7

Step-by-step explanation:

Written in standard form, the equation is ...

  2x² -13x -7 = 0

We observe that factors of (2)(-7) that have a sum of -13 are -14 and +1. Rewriting the middle term using these numbers, we have ...

  2x² -14x +x -7 = 0

  2x(x -7) +1(x -7) = 0 . . . . . factor pairs of terms

  (2x +1)(x -7) = 0 . . . . . . . . factored form

The solutions are the values of x that make these factors zero.

  2x +1 = 0   ⇒   x = -1/2

  x -7 = 0   ⇒   x = 7

The solutions to the quadratic are x = -1/2 and x = 7.