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What are the roots of -x^2 + 4x = -5? Also how do you find the roots of -x^2 + 4x = -5?

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rosey-girl | Student, Grade 12 | (Level 1) Valedictorian

Posted May 15, 2013 at 9:46 PM via web

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What are the roots of -x^2 + 4x = -5?

Also how do you find the roots of -x^2 + 4x = -5?

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violy | High School Teacher | (Level 3) Assistant Educator

Posted May 15, 2013 at 10:18 PM (Answer #1)

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We can rewrite the equation in the form ax^2 + bx + c = 0. 

Add 5 on both sides first.

`-x^2 + 4x + 5 = -5 + 5`

`-x^2 + 4x + 5 = 0`

Multiply both sides by -1 to make the leading coefficient positive.

`x^2 -4x - 5 = 0`

Factor the left side.

`(x - 5)(x + 1) = 0`

Equate each factor to zero, and solve for x.

`x - 5 = 0 ; x + 1 = 0`

`x = 5 ; x = -1`

Hence, roots are: x = {5, -1}.

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