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Simplifying x2 + -40x + 72 = 0 Reorder the terms: 72 + -40x + x2 = 0 Solving 72 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + -40x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + -40x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -40x + x2 = 0 + -72 -40x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 -40x + x2 = -72 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -72 + 400 Reorder the terms: 400 + -40x + x2 = -72 + 400 Combine like terms: -72 + 400 = 328 400 + -40x + x2 = 328 Factor a perfect square on the left side: (x + -20)(x + -20) = 328 Calculate the square root of the right side: 18.110770276 Break this problem into two subproblems by setting (x + -20) equal to 18.110770276 and -18.110770276.Subproblem 1
x + -20 = 18.110770276 Simplifying x + -20 = 18.110770276 Reorder the terms: -20 + x = 18.110770276 Solving -20 + x = 18.110770276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 18.110770276 + 20 Combine like terms: -20 + 20 = 0 0 + x = 18.110770276 + 20 x = 18.110770276 + 20 Combine like terms: 18.110770276 + 20 = 38.110770276 x = 38.110770276 Simplifying x = 38.110770276Subproblem 2
x + -20 = -18.110770276 Simplifying x + -20 = -18.110770276 Reorder the terms: -20 + x = -18.110770276 Solving -20 + x = -18.110770276 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -18.110770276 + 20 Combine like terms: -20 + 20 = 0 0 + x = -18.110770276 + 20 x = -18.110770276 + 20 Combine like terms: -18.110770276 + 20 = 1.889229724 x = 1.889229724 Simplifying x = 1.889229724Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.110770276, 1.889229724}
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