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Simplifying 500 = -10x2 + 255x + -1008 Reorder the terms: 500 = -1008 + 255x + -10x2 Solving 500 = -1008 + 255x + -10x2 Solving for variable 'x'. Combine like terms: 500 + 1008 = 1508 1508 + -255x + 10x2 = -1008 + 255x + -10x2 + 1008 + -255x + 10x2 Reorder the terms: 1508 + -255x + 10x2 = -1008 + 1008 + 255x + -255x + -10x2 + 10x2 Combine like terms: -1008 + 1008 = 0 1508 + -255x + 10x2 = 0 + 255x + -255x + -10x2 + 10x2 1508 + -255x + 10x2 = 255x + -255x + -10x2 + 10x2 Combine like terms: 255x + -255x = 0 1508 + -255x + 10x2 = 0 + -10x2 + 10x2 1508 + -255x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 1508 + -255x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 150.8 + -25.5x + x2 = 0 Move the constant term to the right: Add '-150.8' to each side of the equation. 150.8 + -25.5x + -150.8 + x2 = 0 + -150.8 Reorder the terms: 150.8 + -150.8 + -25.5x + x2 = 0 + -150.8 Combine like terms: 150.8 + -150.8 = 0.0 0.0 + -25.5x + x2 = 0 + -150.8 -25.5x + x2 = 0 + -150.8 Combine like terms: 0 + -150.8 = -150.8 -25.5x + x2 = -150.8 The x term is -25.5x. Take half its coefficient (-12.75). Square it (162.5625) and add it to both sides. Add '162.5625' to each side of the equation. -25.5x + 162.5625 + x2 = -150.8 + 162.5625 Reorder the terms: 162.5625 + -25.5x + x2 = -150.8 + 162.5625 Combine like terms: -150.8 + 162.5625 = 11.7625 162.5625 + -25.5x + x2 = 11.7625 Factor a perfect square on the left side: (x + -12.75)(x + -12.75) = 11.7625 Calculate the square root of the right side: 3.429650128 Break this problem into two subproblems by setting (x + -12.75) equal to 3.429650128 and -3.429650128.Subproblem 1
x + -12.75 = 3.429650128 Simplifying x + -12.75 = 3.429650128 Reorder the terms: -12.75 + x = 3.429650128 Solving -12.75 + x = 3.429650128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.75' to each side of the equation. -12.75 + 12.75 + x = 3.429650128 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + x = 3.429650128 + 12.75 x = 3.429650128 + 12.75 Combine like terms: 3.429650128 + 12.75 = 16.179650128 x = 16.179650128 Simplifying x = 16.179650128Subproblem 2
x + -12.75 = -3.429650128 Simplifying x + -12.75 = -3.429650128 Reorder the terms: -12.75 + x = -3.429650128 Solving -12.75 + x = -3.429650128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.75' to each side of the equation. -12.75 + 12.75 + x = -3.429650128 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + x = -3.429650128 + 12.75 x = -3.429650128 + 12.75 Combine like terms: -3.429650128 + 12.75 = 9.320349872 x = 9.320349872 Simplifying x = 9.320349872Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.179650128, 9.320349872}
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