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Simplifying 225 = 0.092x2 + 0.64x + 150.754 Reorder the terms: 225 = 150.754 + 0.64x + 0.092x2 Solving 225 = 150.754 + 0.64x + 0.092x2 Solving for variable 'x'. Combine like terms: 225 + -150.754 = 74.246 74.246 + -0.64x + -0.092x2 = 150.754 + 0.64x + 0.092x2 + -150.754 + -0.64x + -0.092x2 Reorder the terms: 74.246 + -0.64x + -0.092x2 = 150.754 + -150.754 + 0.64x + -0.64x + 0.092x2 + -0.092x2 Combine like terms: 150.754 + -150.754 = 0.000 74.246 + -0.64x + -0.092x2 = 0.000 + 0.64x + -0.64x + 0.092x2 + -0.092x2 74.246 + -0.64x + -0.092x2 = 0.64x + -0.64x + 0.092x2 + -0.092x2 Combine like terms: 0.64x + -0.64x = 0.00 74.246 + -0.64x + -0.092x2 = 0.00 + 0.092x2 + -0.092x2 74.246 + -0.64x + -0.092x2 = 0.092x2 + -0.092x2 Combine like terms: 0.092x2 + -0.092x2 = 0.000 74.246 + -0.64x + -0.092x2 = 0.000 Begin completing the square. Divide all terms by -0.092 the coefficient of the squared term: Divide each side by '-0.092'. -807.0217391 + 6.956521739x + x2 = 0 Move the constant term to the right: Add '807.0217391' to each side of the equation. -807.0217391 + 6.956521739x + 807.0217391 + x2 = 0 + 807.0217391 Reorder the terms: -807.0217391 + 807.0217391 + 6.956521739x + x2 = 0 + 807.0217391 Combine like terms: -807.0217391 + 807.0217391 = 0.0000000 0.0000000 + 6.956521739x + x2 = 0 + 807.0217391 6.956521739x + x2 = 0 + 807.0217391 Combine like terms: 0 + 807.0217391 = 807.0217391 6.956521739x + x2 = 807.0217391 The x term is 6.956521739x. Take half its coefficient (3.47826087). Square it (12.09829868) and add it to both sides. Add '12.09829868' to each side of the equation. 6.956521739x + 12.09829868 + x2 = 807.0217391 + 12.09829868 Reorder the terms: 12.09829868 + 6.956521739x + x2 = 807.0217391 + 12.09829868 Combine like terms: 807.0217391 + 12.09829868 = 819.12003778 12.09829868 + 6.956521739x + x2 = 819.12003778 Factor a perfect square on the left side: (x + 3.47826087)(x + 3.47826087) = 819.12003778 Calculate the square root of the right side: 28.620273195 Break this problem into two subproblems by setting (x + 3.47826087) equal to 28.620273195 and -28.620273195.Subproblem 1
x + 3.47826087 = 28.620273195 Simplifying x + 3.47826087 = 28.620273195 Reorder the terms: 3.47826087 + x = 28.620273195 Solving 3.47826087 + x = 28.620273195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.47826087' to each side of the equation. 3.47826087 + -3.47826087 + x = 28.620273195 + -3.47826087 Combine like terms: 3.47826087 + -3.47826087 = 0.00000000 0.00000000 + x = 28.620273195 + -3.47826087 x = 28.620273195 + -3.47826087 Combine like terms: 28.620273195 + -3.47826087 = 25.142012325 x = 25.142012325 Simplifying x = 25.142012325Subproblem 2
x + 3.47826087 = -28.620273195 Simplifying x + 3.47826087 = -28.620273195 Reorder the terms: 3.47826087 + x = -28.620273195 Solving 3.47826087 + x = -28.620273195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.47826087' to each side of the equation. 3.47826087 + -3.47826087 + x = -28.620273195 + -3.47826087 Combine like terms: 3.47826087 + -3.47826087 = 0.00000000 0.00000000 + x = -28.620273195 + -3.47826087 x = -28.620273195 + -3.47826087 Combine like terms: -28.620273195 + -3.47826087 = -32.098534065 x = -32.098534065 Simplifying x = -32.098534065Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.142012325, -32.098534065}
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