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Simplifying x2 + -24x + 144 = 14 Reorder the terms: 144 + -24x + x2 = 14 Solving 144 + -24x + x2 = 14 Solving for variable 'x'. Reorder the terms: 144 + -14 + -24x + x2 = 14 + -14 Combine like terms: 144 + -14 = 130 130 + -24x + x2 = 14 + -14 Combine like terms: 14 + -14 = 0 130 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-130' to each side of the equation. 130 + -24x + -130 + x2 = 0 + -130 Reorder the terms: 130 + -130 + -24x + x2 = 0 + -130 Combine like terms: 130 + -130 = 0 0 + -24x + x2 = 0 + -130 -24x + x2 = 0 + -130 Combine like terms: 0 + -130 = -130 -24x + x2 = -130 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -130 + 144 Reorder the terms: 144 + -24x + x2 = -130 + 144 Combine like terms: -130 + 144 = 14 144 + -24x + x2 = 14 Factor a perfect square on the left side: (x + -12)(x + -12) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -12) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -12 = 3.741657387 Simplifying x + -12 = 3.741657387 Reorder the terms: -12 + x = 3.741657387 Solving -12 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 3.741657387 + 12 Combine like terms: -12 + 12 = 0 0 + x = 3.741657387 + 12 x = 3.741657387 + 12 Combine like terms: 3.741657387 + 12 = 15.741657387 x = 15.741657387 Simplifying x = 15.741657387Subproblem 2
x + -12 = -3.741657387 Simplifying x + -12 = -3.741657387 Reorder the terms: -12 + x = -3.741657387 Solving -12 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -3.741657387 + 12 Combine like terms: -12 + 12 = 0 0 + x = -3.741657387 + 12 x = -3.741657387 + 12 Combine like terms: -3.741657387 + 12 = 8.258342613 x = 8.258342613 Simplifying x = 8.258342613Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.741657387, 8.258342613}
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