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Simplifying x2 + -240x + 13600 = 0 Reorder the terms: 13600 + -240x + x2 = 0 Solving 13600 + -240x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-13600' to each side of the equation. 13600 + -240x + -13600 + x2 = 0 + -13600 Reorder the terms: 13600 + -13600 + -240x + x2 = 0 + -13600 Combine like terms: 13600 + -13600 = 0 0 + -240x + x2 = 0 + -13600 -240x + x2 = 0 + -13600 Combine like terms: 0 + -13600 = -13600 -240x + x2 = -13600 The x term is -240x. Take half its coefficient (-120). Square it (14400) and add it to both sides. Add '14400' to each side of the equation. -240x + 14400 + x2 = -13600 + 14400 Reorder the terms: 14400 + -240x + x2 = -13600 + 14400 Combine like terms: -13600 + 14400 = 800 14400 + -240x + x2 = 800 Factor a perfect square on the left side: (x + -120)(x + -120) = 800 Calculate the square root of the right side: 28.284271247 Break this problem into two subproblems by setting (x + -120) equal to 28.284271247 and -28.284271247.Subproblem 1
x + -120 = 28.284271247 Simplifying x + -120 = 28.284271247 Reorder the terms: -120 + x = 28.284271247 Solving -120 + x = 28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + x = 28.284271247 + 120 Combine like terms: -120 + 120 = 0 0 + x = 28.284271247 + 120 x = 28.284271247 + 120 Combine like terms: 28.284271247 + 120 = 148.284271247 x = 148.284271247 Simplifying x = 148.284271247Subproblem 2
x + -120 = -28.284271247 Simplifying x + -120 = -28.284271247 Reorder the terms: -120 + x = -28.284271247 Solving -120 + x = -28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + x = -28.284271247 + 120 Combine like terms: -120 + 120 = 0 0 + x = -28.284271247 + 120 x = -28.284271247 + 120 Combine like terms: -28.284271247 + 120 = 91.715728753 x = 91.715728753 Simplifying x = 91.715728753Solution
The solution to the problem is based on the solutions from the subproblems. x = {148.284271247, 91.715728753}
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