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Simplifying 60 = 0.4x2 + 0.5x Reorder the terms: 60 = 0.5x + 0.4x2 Solving 60 = 0.5x + 0.4x2 Solving for variable 'x'. Reorder the terms: 60 + -0.5x + -0.4x2 = 0.5x + -0.5x + 0.4x2 + -0.4x2 Combine like terms: 0.5x + -0.5x = 0.0 60 + -0.5x + -0.4x2 = 0.0 + 0.4x2 + -0.4x2 60 + -0.5x + -0.4x2 = 0.4x2 + -0.4x2 Combine like terms: 0.4x2 + -0.4x2 = 0.0 60 + -0.5x + -0.4x2 = 0.0 Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. -150 + 1.25x + x2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + 1.25x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 1.25x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 1.25x + x2 = 0 + 150 1.25x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 1.25x + x2 = 150 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 150 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 150 + 0.390625 Combine like terms: 150 + 0.390625 = 150.390625 0.390625 + 1.25x + x2 = 150.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 150.390625 Calculate the square root of the right side: 12.263385544 Break this problem into two subproblems by setting (x + 0.625) equal to 12.263385544 and -12.263385544.Subproblem 1
x + 0.625 = 12.263385544 Simplifying x + 0.625 = 12.263385544 Reorder the terms: 0.625 + x = 12.263385544 Solving 0.625 + x = 12.263385544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 12.263385544 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 12.263385544 + -0.625 x = 12.263385544 + -0.625 Combine like terms: 12.263385544 + -0.625 = 11.638385544 x = 11.638385544 Simplifying x = 11.638385544Subproblem 2
x + 0.625 = -12.263385544 Simplifying x + 0.625 = -12.263385544 Reorder the terms: 0.625 + x = -12.263385544 Solving 0.625 + x = -12.263385544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -12.263385544 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -12.263385544 + -0.625 x = -12.263385544 + -0.625 Combine like terms: -12.263385544 + -0.625 = -12.888385544 x = -12.888385544 Simplifying x = -12.888385544Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.638385544, -12.888385544}
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