7x^2-14x-49=7

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Solution for 7x^2-14x-49=7 equation:


Simplifying
7x2 + -14x + -49 = 7

Reorder the terms:
-49 + -14x + 7x2 = 7

Solving
-49 + -14x + 7x2 = 7

Solving for variable 'x'.

Reorder the terms:
-49 + -7 + -14x + 7x2 = 7 + -7

Combine like terms: -49 + -7 = -56
-56 + -14x + 7x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-56 + -14x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-8 + -2x + x2) = 0

Factor a trinomial.
7((-2 + -1x)(4 + -1x)) = 0

Ignore the factor 7.

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-2, 4}

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