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Simplifying x2 + -136x + 64 = 0 Reorder the terms: 64 + -136x + x2 = 0 Solving 64 + -136x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + -136x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + -136x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -136x + x2 = 0 + -64 -136x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 -136x + x2 = -64 The x term is -136x. Take half its coefficient (-68). Square it (4624) and add it to both sides. Add '4624' to each side of the equation. -136x + 4624 + x2 = -64 + 4624 Reorder the terms: 4624 + -136x + x2 = -64 + 4624 Combine like terms: -64 + 4624 = 4560 4624 + -136x + x2 = 4560 Factor a perfect square on the left side: (x + -68)(x + -68) = 4560 Calculate the square root of the right side: 67.527772065 Break this problem into two subproblems by setting (x + -68) equal to 67.527772065 and -67.527772065.Subproblem 1
x + -68 = 67.527772065 Simplifying x + -68 = 67.527772065 Reorder the terms: -68 + x = 67.527772065 Solving -68 + x = 67.527772065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68' to each side of the equation. -68 + 68 + x = 67.527772065 + 68 Combine like terms: -68 + 68 = 0 0 + x = 67.527772065 + 68 x = 67.527772065 + 68 Combine like terms: 67.527772065 + 68 = 135.527772065 x = 135.527772065 Simplifying x = 135.527772065Subproblem 2
x + -68 = -67.527772065 Simplifying x + -68 = -67.527772065 Reorder the terms: -68 + x = -67.527772065 Solving -68 + x = -67.527772065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68' to each side of the equation. -68 + 68 + x = -67.527772065 + 68 Combine like terms: -68 + 68 = 0 0 + x = -67.527772065 + 68 x = -67.527772065 + 68 Combine like terms: -67.527772065 + 68 = 0.472227935 x = 0.472227935 Simplifying x = 0.472227935Solution
The solution to the problem is based on the solutions from the subproblems. x = {135.527772065, 0.472227935}
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