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Simplifying x2 + -40x + -117 = 0 Reorder the terms: -117 + -40x + x2 = 0 Solving -117 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '117' to each side of the equation. -117 + -40x + 117 + x2 = 0 + 117 Reorder the terms: -117 + 117 + -40x + x2 = 0 + 117 Combine like terms: -117 + 117 = 0 0 + -40x + x2 = 0 + 117 -40x + x2 = 0 + 117 Combine like terms: 0 + 117 = 117 -40x + x2 = 117 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 = 117 + 400 Reorder the terms: 400 + -40x + x2 = 117 + 400 Combine like terms: 117 + 400 = 517 400 + -40x + x2 = 517 Factor a perfect square on the left side: (x + -20)(x + -20) = 517 Calculate the square root of the right side: 22.737634002 Break this problem into two subproblems by setting (x + -20) equal to 22.737634002 and -22.737634002.Subproblem 1
x + -20 = 22.737634002 Simplifying x + -20 = 22.737634002 Reorder the terms: -20 + x = 22.737634002 Solving -20 + x = 22.737634002 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 = 22.737634002 + 20 Combine like terms: -20 + 20 = 0 0 + x = 22.737634002 + 20 x = 22.737634002 + 20 Combine like terms: 22.737634002 + 20 = 42.737634002 x = 42.737634002 Simplifying x = 42.737634002Subproblem 2
x + -20 = -22.737634002 Simplifying x + -20 = -22.737634002 Reorder the terms: -20 + x = -22.737634002 Solving -20 + x = -22.737634002 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 = -22.737634002 + 20 Combine like terms: -20 + 20 = 0 0 + x = -22.737634002 + 20 x = -22.737634002 + 20 Combine like terms: -22.737634002 + 20 = -2.737634002 x = -2.737634002 Simplifying x = -2.737634002Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.737634002, -2.737634002}
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