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Simplifying 1000 + -1x = 800(x2) Solving 1000 + -1x = 800x2 Solving for variable 'x'. Combine like terms: 800x2 + -800x2 = 0 1000 + -1x + -800x2 = 0 Begin completing the square. Divide all terms by -800 the coefficient of the squared term: Divide each side by '-800'. -1.25 + 0.00125x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.00125x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.00125x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.00125x + x2 = 0 + 1.25 0.00125x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.00125x + x2 = 1.25 The x term is 0.00125x. Take half its coefficient (0.000625). Square it (0.000000390625) and add it to both sides. Add '0.000000390625' to each side of the equation. 0.00125x + 0.000000390625 + x2 = 1.25 + 0.000000390625 Reorder the terms: 0.000000390625 + 0.00125x + x2 = 1.25 + 0.000000390625 Combine like terms: 1.25 + 0.000000390625 = 1.250000390625 0.000000390625 + 0.00125x + x2 = 1.250000390625 Factor a perfect square on the left side: (x + 0.000625)(x + 0.000625) = 1.250000390625 Calculate the square root of the right side: 1.118034163 Break this problem into two subproblems by setting (x + 0.000625) equal to 1.118034163 and -1.118034163.Subproblem 1
x + 0.000625 = 1.118034163 Simplifying x + 0.000625 = 1.118034163 Reorder the terms: 0.000625 + x = 1.118034163 Solving 0.000625 + x = 1.118034163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000625' to each side of the equation. 0.000625 + -0.000625 + x = 1.118034163 + -0.000625 Combine like terms: 0.000625 + -0.000625 = 0.000000 0.000000 + x = 1.118034163 + -0.000625 x = 1.118034163 + -0.000625 Combine like terms: 1.118034163 + -0.000625 = 1.117409163 x = 1.117409163 Simplifying x = 1.117409163Subproblem 2
x + 0.000625 = -1.118034163 Simplifying x + 0.000625 = -1.118034163 Reorder the terms: 0.000625 + x = -1.118034163 Solving 0.000625 + x = -1.118034163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000625' to each side of the equation. 0.000625 + -0.000625 + x = -1.118034163 + -0.000625 Combine like terms: 0.000625 + -0.000625 = 0.000000 0.000000 + x = -1.118034163 + -0.000625 x = -1.118034163 + -0.000625 Combine like terms: -1.118034163 + -0.000625 = -1.118659163 x = -1.118659163 Simplifying x = -1.118659163Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.117409163, -1.118659163}
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