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Simplifying
84(x + 1) = (85 + x)(x + -1)
Reorder the terms:
84(1 + x) = (85 + x)(x + -1)
(1 * 84 + x * 84) = (85 + x)(x + -1)
(84 + 84x) = (85 + x)(x + -1)
Reorder the terms:
84 + 84x = (85 + x)(-1 + x)
Multiply (85 + x) * (-1 + x)
84 + 84x = (85(-1 + x) + x(-1 + x))
84 + 84x = ((-1 * 85 + x * 85) + x(-1 + x))
84 + 84x = ((-85 + 85x) + x(-1 + x))
84 + 84x = (-85 + 85x + (-1 * x + x * x))
84 + 84x = (-85 + 85x + (-1x + x2))
Combine like terms: 85x + -1x = 84x
84 + 84x = (-85 + 84x + x2)
Add '-84x' to each side of the equation.
84 + 84x + -84x = -85 + 84x + -84x + x2
Combine like terms: 84x + -84x = 0
84 + 0 = -85 + 84x + -84x + x2
84 = -85 + 84x + -84x + x2
Combine like terms: 84x + -84x = 0
84 = -85 + 0 + x2
84 = -85 + x2
Solving
84 = -85 + x2
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1x2' to each side of the equation.
84 + -1x2 = -85 + x2 + -1x2
Combine like terms: x2 + -1x2 = 0
84 + -1x2 = -85 + 0
84 + -1x2 = -85
Add '-84' to each side of the equation.
84 + -84 + -1x2 = -85 + -84
Combine like terms: 84 + -84 = 0
0 + -1x2 = -85 + -84
-1x2 = -85 + -84
Combine like terms: -85 + -84 = -169
-1x2 = -169
Divide each side by '-1'.
x2 = 169
Simplifying
x2 = 169
Take the square root of each side:
x = {-13, 13}
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