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Simplifying x2 + -40x + -412 = 0 Reorder the terms: -412 + -40x + x2 = 0 Solving -412 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '412' to each side of the equation. -412 + -40x + 412 + x2 = 0 + 412 Reorder the terms: -412 + 412 + -40x + x2 = 0 + 412 Combine like terms: -412 + 412 = 0 0 + -40x + x2 = 0 + 412 -40x + x2 = 0 + 412 Combine like terms: 0 + 412 = 412 -40x + x2 = 412 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 = 412 + 400 Reorder the terms: 400 + -40x + x2 = 412 + 400 Combine like terms: 412 + 400 = 812 400 + -40x + x2 = 812 Factor a perfect square on the left side: (x + -20)(x + -20) = 812 Calculate the square root of the right side: 28.495613698 Break this problem into two subproblems by setting (x + -20) equal to 28.495613698 and -28.495613698.Subproblem 1
x + -20 = 28.495613698 Simplifying x + -20 = 28.495613698 Reorder the terms: -20 + x = 28.495613698 Solving -20 + x = 28.495613698 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 = 28.495613698 + 20 Combine like terms: -20 + 20 = 0 0 + x = 28.495613698 + 20 x = 28.495613698 + 20 Combine like terms: 28.495613698 + 20 = 48.495613698 x = 48.495613698 Simplifying x = 48.495613698Subproblem 2
x + -20 = -28.495613698 Simplifying x + -20 = -28.495613698 Reorder the terms: -20 + x = -28.495613698 Solving -20 + x = -28.495613698 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 = -28.495613698 + 20 Combine like terms: -20 + 20 = 0 0 + x = -28.495613698 + 20 x = -28.495613698 + 20 Combine like terms: -28.495613698 + 20 = -8.495613698 x = -8.495613698 Simplifying x = -8.495613698Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.495613698, -8.495613698}
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