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Simplifying (x) = -1.2x2 + 62.5x + -491 x = -1.2x2 + 62.5x + -491 Reorder the terms: x = -491 + 62.5x + -1.2x2 Solving x = -491 + 62.5x + -1.2x2 Solving for variable 'x'. Reorder the terms: 491 + x + -62.5x + 1.2x2 = -491 + 62.5x + -1.2x2 + 491 + -62.5x + 1.2x2 Combine like terms: x + -62.5x = -61.5x 491 + -61.5x + 1.2x2 = -491 + 62.5x + -1.2x2 + 491 + -62.5x + 1.2x2 Reorder the terms: 491 + -61.5x + 1.2x2 = -491 + 491 + 62.5x + -62.5x + -1.2x2 + 1.2x2 Combine like terms: -491 + 491 = 0 491 + -61.5x + 1.2x2 = 0 + 62.5x + -62.5x + -1.2x2 + 1.2x2 491 + -61.5x + 1.2x2 = 62.5x + -62.5x + -1.2x2 + 1.2x2 Combine like terms: 62.5x + -62.5x = 0.0 491 + -61.5x + 1.2x2 = 0.0 + -1.2x2 + 1.2x2 491 + -61.5x + 1.2x2 = -1.2x2 + 1.2x2 Combine like terms: -1.2x2 + 1.2x2 = 0.0 491 + -61.5x + 1.2x2 = 0.0 Begin completing the square. Divide all terms by 1.2 the coefficient of the squared term: Divide each side by '1.2'. 409.1666667 + -51.25x + x2 = 0 Move the constant term to the right: Add '-409.1666667' to each side of the equation. 409.1666667 + -51.25x + -409.1666667 + x2 = 0 + -409.1666667 Reorder the terms: 409.1666667 + -409.1666667 + -51.25x + x2 = 0 + -409.1666667 Combine like terms: 409.1666667 + -409.1666667 = 0.0000000 0.0000000 + -51.25x + x2 = 0 + -409.1666667 -51.25x + x2 = 0 + -409.1666667 Combine like terms: 0 + -409.1666667 = -409.1666667 -51.25x + x2 = -409.1666667 The x term is -51.25x. Take half its coefficient (-25.625). Square it (656.640625) and add it to both sides. Add '656.640625' to each side of the equation. -51.25x + 656.640625 + x2 = -409.1666667 + 656.640625 Reorder the terms: 656.640625 + -51.25x + x2 = -409.1666667 + 656.640625 Combine like terms: -409.1666667 + 656.640625 = 247.4739583 656.640625 + -51.25x + x2 = 247.4739583 Factor a perfect square on the left side: (x + -25.625)(x + -25.625) = 247.4739583 Calculate the square root of the right side: 15.731305041 Break this problem into two subproblems by setting (x + -25.625) equal to 15.731305041 and -15.731305041.Subproblem 1
x + -25.625 = 15.731305041 Simplifying x + -25.625 = 15.731305041 Reorder the terms: -25.625 + x = 15.731305041 Solving -25.625 + x = 15.731305041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.625' to each side of the equation. -25.625 + 25.625 + x = 15.731305041 + 25.625 Combine like terms: -25.625 + 25.625 = 0.000 0.000 + x = 15.731305041 + 25.625 x = 15.731305041 + 25.625 Combine like terms: 15.731305041 + 25.625 = 41.356305041 x = 41.356305041 Simplifying x = 41.356305041Subproblem 2
x + -25.625 = -15.731305041 Simplifying x + -25.625 = -15.731305041 Reorder the terms: -25.625 + x = -15.731305041 Solving -25.625 + x = -15.731305041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.625' to each side of the equation. -25.625 + 25.625 + x = -15.731305041 + 25.625 Combine like terms: -25.625 + 25.625 = 0.000 0.000 + x = -15.731305041 + 25.625 x = -15.731305041 + 25.625 Combine like terms: -15.731305041 + 25.625 = 9.893694959 x = 9.893694959 Simplifying x = 9.893694959Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.356305041, 9.893694959}
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