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Simplifying 267 = 0.125x2 + -0.8x + 99 Reorder the terms: 267 = 99 + -0.8x + 0.125x2 Solving 267 = 99 + -0.8x + 0.125x2 Solving for variable 'x'. Combine like terms: 267 + -99 = 168 168 + 0.8x + -0.125x2 = 99 + -0.8x + 0.125x2 + -99 + 0.8x + -0.125x2 Reorder the terms: 168 + 0.8x + -0.125x2 = 99 + -99 + -0.8x + 0.8x + 0.125x2 + -0.125x2 Combine like terms: 99 + -99 = 0 168 + 0.8x + -0.125x2 = 0 + -0.8x + 0.8x + 0.125x2 + -0.125x2 168 + 0.8x + -0.125x2 = -0.8x + 0.8x + 0.125x2 + -0.125x2 Combine like terms: -0.8x + 0.8x = 0.0 168 + 0.8x + -0.125x2 = 0.0 + 0.125x2 + -0.125x2 168 + 0.8x + -0.125x2 = 0.125x2 + -0.125x2 Combine like terms: 0.125x2 + -0.125x2 = 0.000 168 + 0.8x + -0.125x2 = 0.000 Begin completing the square. Divide all terms by -0.125 the coefficient of the squared term: Divide each side by '-0.125'. -1344 + -6.4x + x2 = 0 Move the constant term to the right: Add '1344' to each side of the equation. -1344 + -6.4x + 1344 + x2 = 0 + 1344 Reorder the terms: -1344 + 1344 + -6.4x + x2 = 0 + 1344 Combine like terms: -1344 + 1344 = 0 0 + -6.4x + x2 = 0 + 1344 -6.4x + x2 = 0 + 1344 Combine like terms: 0 + 1344 = 1344 -6.4x + x2 = 1344 The x term is -6.4x. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4x + 10.24 + x2 = 1344 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = 1344 + 10.24 Combine like terms: 1344 + 10.24 = 1354.24 10.24 + -6.4x + x2 = 1354.24 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 1354.24 Calculate the square root of the right side: 36.8 Break this problem into two subproblems by setting (x + -3.2) equal to 36.8 and -36.8.Subproblem 1
x + -3.2 = 36.8 Simplifying x + -3.2 = 36.8 Reorder the terms: -3.2 + x = 36.8 Solving -3.2 + x = 36.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = 36.8 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 36.8 + 3.2 x = 36.8 + 3.2 Combine like terms: 36.8 + 3.2 = 40 x = 40 Simplifying x = 40Subproblem 2
x + -3.2 = -36.8 Simplifying x + -3.2 = -36.8 Reorder the terms: -3.2 + x = -36.8 Solving -3.2 + x = -36.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = -36.8 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -36.8 + 3.2 x = -36.8 + 3.2 Combine like terms: -36.8 + 3.2 = -33.6 x = -33.6 Simplifying x = -33.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {40, -33.6}
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