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Simplifying x2 + -112x + 120 = 0 Reorder the terms: 120 + -112x + x2 = 0 Solving 120 + -112x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + -112x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + -112x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + -112x + x2 = 0 + -120 -112x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 -112x + x2 = -120 The x term is -112x. Take half its coefficient (-56). Square it (3136) and add it to both sides. Add '3136' to each side of the equation. -112x + 3136 + x2 = -120 + 3136 Reorder the terms: 3136 + -112x + x2 = -120 + 3136 Combine like terms: -120 + 3136 = 3016 3136 + -112x + x2 = 3016 Factor a perfect square on the left side: (x + -56)(x + -56) = 3016 Calculate the square root of the right side: 54.918120871 Break this problem into two subproblems by setting (x + -56) equal to 54.918120871 and -54.918120871.Subproblem 1
x + -56 = 54.918120871 Simplifying x + -56 = 54.918120871 Reorder the terms: -56 + x = 54.918120871 Solving -56 + x = 54.918120871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + x = 54.918120871 + 56 Combine like terms: -56 + 56 = 0 0 + x = 54.918120871 + 56 x = 54.918120871 + 56 Combine like terms: 54.918120871 + 56 = 110.918120871 x = 110.918120871 Simplifying x = 110.918120871Subproblem 2
x + -56 = -54.918120871 Simplifying x + -56 = -54.918120871 Reorder the terms: -56 + x = -54.918120871 Solving -56 + x = -54.918120871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '56' to each side of the equation. -56 + 56 + x = -54.918120871 + 56 Combine like terms: -56 + 56 = 0 0 + x = -54.918120871 + 56 x = -54.918120871 + 56 Combine like terms: -54.918120871 + 56 = 1.081879129 x = 1.081879129 Simplifying x = 1.081879129Solution
The solution to the problem is based on the solutions from the subproblems. x = {110.918120871, 1.081879129}
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