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Simplifying x = 0.5x2 + 10x + -400 Reorder the terms: x = -400 + 10x + 0.5x2 Solving x = -400 + 10x + 0.5x2 Solving for variable 'x'. Reorder the terms: 400 + x + -10x + -0.5x2 = -400 + 10x + 0.5x2 + 400 + -10x + -0.5x2 Combine like terms: x + -10x = -9x 400 + -9x + -0.5x2 = -400 + 10x + 0.5x2 + 400 + -10x + -0.5x2 Reorder the terms: 400 + -9x + -0.5x2 = -400 + 400 + 10x + -10x + 0.5x2 + -0.5x2 Combine like terms: -400 + 400 = 0 400 + -9x + -0.5x2 = 0 + 10x + -10x + 0.5x2 + -0.5x2 400 + -9x + -0.5x2 = 10x + -10x + 0.5x2 + -0.5x2 Combine like terms: 10x + -10x = 0 400 + -9x + -0.5x2 = 0 + 0.5x2 + -0.5x2 400 + -9x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 400 + -9x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -800 + 18x + x2 = 0 Move the constant term to the right: Add '800' to each side of the equation. -800 + 18x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + 18x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + 18x + x2 = 0 + 800 18x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 18x + x2 = 800 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 800 + 81 Reorder the terms: 81 + 18x + x2 = 800 + 81 Combine like terms: 800 + 81 = 881 81 + 18x + x2 = 881 Factor a perfect square on the left side: (x + 9)(x + 9) = 881 Calculate the square root of the right side: 29.681644159 Break this problem into two subproblems by setting (x + 9) equal to 29.681644159 and -29.681644159.Subproblem 1
x + 9 = 29.681644159 Simplifying x + 9 = 29.681644159 Reorder the terms: 9 + x = 29.681644159 Solving 9 + x = 29.681644159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 29.681644159 + -9 Combine like terms: 9 + -9 = 0 0 + x = 29.681644159 + -9 x = 29.681644159 + -9 Combine like terms: 29.681644159 + -9 = 20.681644159 x = 20.681644159 Simplifying x = 20.681644159Subproblem 2
x + 9 = -29.681644159 Simplifying x + 9 = -29.681644159 Reorder the terms: 9 + x = -29.681644159 Solving 9 + x = -29.681644159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -29.681644159 + -9 Combine like terms: 9 + -9 = 0 0 + x = -29.681644159 + -9 x = -29.681644159 + -9 Combine like terms: -29.681644159 + -9 = -38.681644159 x = -38.681644159 Simplifying x = -38.681644159Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.681644159, -38.681644159}
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