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Simplifying 8x2 + -1x + -10000 = 0 Reorder the terms: -10000 + -1x + 8x2 = 0 Solving -10000 + -1x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1250 + -0.125x + x2 = 0 Move the constant term to the right: Add '1250' to each side of the equation. -1250 + -0.125x + 1250 + x2 = 0 + 1250 Reorder the terms: -1250 + 1250 + -0.125x + x2 = 0 + 1250 Combine like terms: -1250 + 1250 = 0 0 + -0.125x + x2 = 0 + 1250 -0.125x + x2 = 0 + 1250 Combine like terms: 0 + 1250 = 1250 -0.125x + x2 = 1250 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 1250 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 1250 + 0.00390625 Combine like terms: 1250 + 0.00390625 = 1250.00390625 0.00390625 + -0.125x + x2 = 1250.00390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 1250.00390625 Calculate the square root of the right side: 35.355394302 Break this problem into two subproblems by setting (x + -0.0625) equal to 35.355394302 and -35.355394302.Subproblem 1
x + -0.0625 = 35.355394302 Simplifying x + -0.0625 = 35.355394302 Reorder the terms: -0.0625 + x = 35.355394302 Solving -0.0625 + x = 35.355394302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 35.355394302 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 35.355394302 + 0.0625 x = 35.355394302 + 0.0625 Combine like terms: 35.355394302 + 0.0625 = 35.417894302 x = 35.417894302 Simplifying x = 35.417894302Subproblem 2
x + -0.0625 = -35.355394302 Simplifying x + -0.0625 = -35.355394302 Reorder the terms: -0.0625 + x = -35.355394302 Solving -0.0625 + x = -35.355394302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -35.355394302 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -35.355394302 + 0.0625 x = -35.355394302 + 0.0625 Combine like terms: -35.355394302 + 0.0625 = -35.292894302 x = -35.292894302 Simplifying x = -35.292894302Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.417894302, -35.292894302}
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