8(x-13)(x-13)=104

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Solution for 8(x-13)(x-13)=104 equation:


Simplifying
8(x + -13)(x + -13) = 104

Reorder the terms:
8(-13 + x)(x + -13) = 104

Reorder the terms:
8(-13 + x)(-13 + x) = 104

Multiply (-13 + x) * (-13 + x)
8(-13(-13 + x) + x(-13 + x)) = 104
8((-13 * -13 + x * -13) + x(-13 + x)) = 104
8((169 + -13x) + x(-13 + x)) = 104
8(169 + -13x + (-13 * x + x * x)) = 104
8(169 + -13x + (-13x + x2)) = 104

Combine like terms: -13x + -13x = -26x
8(169 + -26x + x2) = 104
(169 * 8 + -26x * 8 + x2 * 8) = 104
(1352 + -208x + 8x2) = 104

Solving
1352 + -208x + 8x2 = 104

Solving for variable 'x'.

Reorder the terms:
1352 + -104 + -208x + 8x2 = 104 + -104

Combine like terms: 1352 + -104 = 1248
1248 + -208x + 8x2 = 104 + -104

Combine like terms: 104 + -104 = 0
1248 + -208x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(156 + -26x + x2) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(156 + -26x + x2)' equal to zero and attempt to solve: Simplifying 156 + -26x + x2 = 0 Solving 156 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-156' to each side of the equation. 156 + -26x + -156 + x2 = 0 + -156 Reorder the terms: 156 + -156 + -26x + x2 = 0 + -156 Combine like terms: 156 + -156 = 0 0 + -26x + x2 = 0 + -156 -26x + x2 = 0 + -156 Combine like terms: 0 + -156 = -156 -26x + x2 = -156 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -156 + 169 Reorder the terms: 169 + -26x + x2 = -156 + 169 Combine like terms: -156 + 169 = 13 169 + -26x + x2 = 13 Factor a perfect square on the left side: (x + -13)(x + -13) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + -13) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + -13 = 3.605551275 Simplifying x + -13 = 3.605551275 Reorder the terms: -13 + x = 3.605551275 Solving -13 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 3.605551275 + 13 Combine like terms: -13 + 13 = 0 0 + x = 3.605551275 + 13 x = 3.605551275 + 13 Combine like terms: 3.605551275 + 13 = 16.605551275 x = 16.605551275 Simplifying x = 16.605551275

Subproblem 2

x + -13 = -3.605551275 Simplifying x + -13 = -3.605551275 Reorder the terms: -13 + x = -3.605551275 Solving -13 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -3.605551275 + 13 Combine like terms: -13 + 13 = 0 0 + x = -3.605551275 + 13 x = -3.605551275 + 13 Combine like terms: -3.605551275 + 13 = 9.394448725 x = 9.394448725 Simplifying x = 9.394448725

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.605551275, 9.394448725}

Solution

x = {16.605551275, 9.394448725}

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