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Simplifying 350 = 0.459041x2 + -3.51099x + 232.359 Reorder the terms: 350 = 232.359 + -3.51099x + 0.459041x2 Solving 350 = 232.359 + -3.51099x + 0.459041x2 Solving for variable 'x'. Combine like terms: 350 + -232.359 = 117.641 117.641 + 3.51099x + -0.459041x2 = 232.359 + -3.51099x + 0.459041x2 + -232.359 + 3.51099x + -0.459041x2 Reorder the terms: 117.641 + 3.51099x + -0.459041x2 = 232.359 + -232.359 + -3.51099x + 3.51099x + 0.459041x2 + -0.459041x2 Combine like terms: 232.359 + -232.359 = 0.000 117.641 + 3.51099x + -0.459041x2 = 0.000 + -3.51099x + 3.51099x + 0.459041x2 + -0.459041x2 117.641 + 3.51099x + -0.459041x2 = -3.51099x + 3.51099x + 0.459041x2 + -0.459041x2 Combine like terms: -3.51099x + 3.51099x = 0.00000 117.641 + 3.51099x + -0.459041x2 = 0.00000 + 0.459041x2 + -0.459041x2 117.641 + 3.51099x + -0.459041x2 = 0.459041x2 + -0.459041x2 Combine like terms: 0.459041x2 + -0.459041x2 = 0.000000 117.641 + 3.51099x + -0.459041x2 = 0.000000 Begin completing the square. Divide all terms by -0.459041 the coefficient of the squared term: Divide each side by '-0.459041'. -256.2755832 + -7.648532484x + x2 = 0 Move the constant term to the right: Add '256.2755832' to each side of the equation. -256.2755832 + -7.648532484x + 256.2755832 + x2 = 0 + 256.2755832 Reorder the terms: -256.2755832 + 256.2755832 + -7.648532484x + x2 = 0 + 256.2755832 Combine like terms: -256.2755832 + 256.2755832 = 0.0000000 0.0000000 + -7.648532484x + x2 = 0 + 256.2755832 -7.648532484x + x2 = 0 + 256.2755832 Combine like terms: 0 + 256.2755832 = 256.2755832 -7.648532484x + x2 = 256.2755832 The x term is -7.648532484x. Take half its coefficient (-3.824266242). Square it (14.62501229) and add it to both sides. Add '14.62501229' to each side of the equation. -7.648532484x + 14.62501229 + x2 = 256.2755832 + 14.62501229 Reorder the terms: 14.62501229 + -7.648532484x + x2 = 256.2755832 + 14.62501229 Combine like terms: 256.2755832 + 14.62501229 = 270.90059549 14.62501229 + -7.648532484x + x2 = 270.90059549 Factor a perfect square on the left side: (x + -3.824266242)(x + -3.824266242) = 270.90059549 Calculate the square root of the right side: 16.459058159 Break this problem into two subproblems by setting (x + -3.824266242) equal to 16.459058159 and -16.459058159.Subproblem 1
x + -3.824266242 = 16.459058159 Simplifying x + -3.824266242 = 16.459058159 Reorder the terms: -3.824266242 + x = 16.459058159 Solving -3.824266242 + x = 16.459058159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.824266242' to each side of the equation. -3.824266242 + 3.824266242 + x = 16.459058159 + 3.824266242 Combine like terms: -3.824266242 + 3.824266242 = 0.000000000 0.000000000 + x = 16.459058159 + 3.824266242 x = 16.459058159 + 3.824266242 Combine like terms: 16.459058159 + 3.824266242 = 20.283324401 x = 20.283324401 Simplifying x = 20.283324401Subproblem 2
x + -3.824266242 = -16.459058159 Simplifying x + -3.824266242 = -16.459058159 Reorder the terms: -3.824266242 + x = -16.459058159 Solving -3.824266242 + x = -16.459058159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.824266242' to each side of the equation. -3.824266242 + 3.824266242 + x = -16.459058159 + 3.824266242 Combine like terms: -3.824266242 + 3.824266242 = 0.000000000 0.000000000 + x = -16.459058159 + 3.824266242 x = -16.459058159 + 3.824266242 Combine like terms: -16.459058159 + 3.824266242 = -12.634791917 x = -12.634791917 Simplifying x = -12.634791917Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.283324401, -12.634791917}
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