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Simplifying 0 = 250 + -9x + -1x2 + 112 Reorder the terms: 0 = 250 + 112 + -9x + -1x2 Combine like terms: 250 + 112 = 362 0 = 362 + -9x + -1x2 Solving 0 = 362 + -9x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -362 = -362 -362 + 9x + x2 = 362 + -9x + -1x2 + -362 + 9x + x2 Reorder the terms: -362 + 9x + x2 = 362 + -362 + -9x + 9x + -1x2 + x2 Combine like terms: 362 + -362 = 0 -362 + 9x + x2 = 0 + -9x + 9x + -1x2 + x2 -362 + 9x + x2 = -9x + 9x + -1x2 + x2 Combine like terms: -9x + 9x = 0 -362 + 9x + x2 = 0 + -1x2 + x2 -362 + 9x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -362 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '362' to each side of the equation. -362 + 9x + 362 + x2 = 0 + 362 Reorder the terms: -362 + 362 + 9x + x2 = 0 + 362 Combine like terms: -362 + 362 = 0 0 + 9x + x2 = 0 + 362 9x + x2 = 0 + 362 Combine like terms: 0 + 362 = 362 9x + x2 = 362 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 362 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 362 + 20.25 Combine like terms: 362 + 20.25 = 382.25 20.25 + 9x + x2 = 382.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 382.25 Calculate the square root of the right side: 19.551214796 Break this problem into two subproblems by setting (x + 4.5) equal to 19.551214796 and -19.551214796.Subproblem 1
x + 4.5 = 19.551214796 Simplifying x + 4.5 = 19.551214796 Reorder the terms: 4.5 + x = 19.551214796 Solving 4.5 + x = 19.551214796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 19.551214796 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 19.551214796 + -4.5 x = 19.551214796 + -4.5 Combine like terms: 19.551214796 + -4.5 = 15.051214796 x = 15.051214796 Simplifying x = 15.051214796Subproblem 2
x + 4.5 = -19.551214796 Simplifying x + 4.5 = -19.551214796 Reorder the terms: 4.5 + x = -19.551214796 Solving 4.5 + x = -19.551214796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -19.551214796 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -19.551214796 + -4.5 x = -19.551214796 + -4.5 Combine like terms: -19.551214796 + -4.5 = -24.051214796 x = -24.051214796 Simplifying x = -24.051214796Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.051214796, -24.051214796}
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