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Simplifying x2 + -800 + -40x = 0 Reorder the terms: -800 + -40x + x2 = 0 Solving -800 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '800' to each side of the equation. -800 + -40x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + -40x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + -40x + x2 = 0 + 800 -40x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 -40x + x2 = 800 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 = 800 + 400 Reorder the terms: 400 + -40x + x2 = 800 + 400 Combine like terms: 800 + 400 = 1200 400 + -40x + x2 = 1200 Factor a perfect square on the left side: (x + -20)(x + -20) = 1200 Calculate the square root of the right side: 34.641016151 Break this problem into two subproblems by setting (x + -20) equal to 34.641016151 and -34.641016151.Subproblem 1
x + -20 = 34.641016151 Simplifying x + -20 = 34.641016151 Reorder the terms: -20 + x = 34.641016151 Solving -20 + x = 34.641016151 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 = 34.641016151 + 20 Combine like terms: -20 + 20 = 0 0 + x = 34.641016151 + 20 x = 34.641016151 + 20 Combine like terms: 34.641016151 + 20 = 54.641016151 x = 54.641016151 Simplifying x = 54.641016151Subproblem 2
x + -20 = -34.641016151 Simplifying x + -20 = -34.641016151 Reorder the terms: -20 + x = -34.641016151 Solving -20 + x = -34.641016151 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 = -34.641016151 + 20 Combine like terms: -20 + 20 = 0 0 + x = -34.641016151 + 20 x = -34.641016151 + 20 Combine like terms: -34.641016151 + 20 = -14.641016151 x = -14.641016151 Simplifying x = -14.641016151Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.641016151, -14.641016151}
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