[x^2+7x-71]=27

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Solution for [x^2+7x-71]=27 equation:


Simplifying
[x2 + 7x + -71] = 27

Reorder the terms:
[-71 + 7x + x2] = 27

Remove brackets around [-71 + 7x + x2]
-71 + 7x + x2 = 27

Solving
-71 + 7x + x2 = 27

Solving for variable 'x'.

Reorder the terms:
-71 + -27 + 7x + x2 = 27 + -27

Combine like terms: -71 + -27 = -98
-98 + 7x + x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-98 + 7x + x2 = 0

Factor a trinomial.
(-14 + -1x)(7 + -1x) = 0

Subproblem 1

Set the factor '(-14 + -1x)' equal to zero and attempt to solve: Simplifying -14 + -1x = 0 Solving -14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1x = 0 + 14 -1x = 0 + 14 Combine like terms: 0 + 14 = 14 -1x = 14 Divide each side by '-1'. x = -14 Simplifying x = -14

Subproblem 2

Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7

Solution

x = {-14, 7}

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