(x-6)(x-8)=-1

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Solution for (x-6)(x-8)=-1 equation:


Simplifying
(x + -6)(x + -8) = -1

Reorder the terms:
(-6 + x)(x + -8) = -1

Reorder the terms:
(-6 + x)(-8 + x) = -1

Multiply (-6 + x) * (-8 + x)
(-6(-8 + x) + x(-8 + x)) = -1
((-8 * -6 + x * -6) + x(-8 + x)) = -1
((48 + -6x) + x(-8 + x)) = -1
(48 + -6x + (-8 * x + x * x)) = -1
(48 + -6x + (-8x + x2)) = -1

Combine like terms: -6x + -8x = -14x
(48 + -14x + x2) = -1

Solving
48 + -14x + x2 = -1

Solving for variable 'x'.

Reorder the terms:
48 + 1 + -14x + x2 = -1 + 1

Combine like terms: 48 + 1 = 49
49 + -14x + x2 = -1 + 1

Combine like terms: -1 + 1 = 0
49 + -14x + x2 = 0

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

Subproblem 1

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

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 = {7, 7}

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