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Simplifying 150x + -8x2 + -670 = 0 Reorder the terms: -670 + 150x + -8x2 = 0 Solving -670 + 150x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-335 + 75x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-335 + 75x + -4x2)' equal to zero and attempt to solve: Simplifying -335 + 75x + -4x2 = 0 Solving -335 + 75x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 83.75 + -18.75x + x2 = 0 Move the constant term to the right: Add '-83.75' to each side of the equation. 83.75 + -18.75x + -83.75 + x2 = 0 + -83.75 Reorder the terms: 83.75 + -83.75 + -18.75x + x2 = 0 + -83.75 Combine like terms: 83.75 + -83.75 = 0.00 0.00 + -18.75x + x2 = 0 + -83.75 -18.75x + x2 = 0 + -83.75 Combine like terms: 0 + -83.75 = -83.75 -18.75x + x2 = -83.75 The x term is -18.75x. Take half its coefficient (-9.375). Square it (87.890625) and add it to both sides. Add '87.890625' to each side of the equation. -18.75x + 87.890625 + x2 = -83.75 + 87.890625 Reorder the terms: 87.890625 + -18.75x + x2 = -83.75 + 87.890625 Combine like terms: -83.75 + 87.890625 = 4.140625 87.890625 + -18.75x + x2 = 4.140625 Factor a perfect square on the left side: (x + -9.375)(x + -9.375) = 4.140625 Calculate the square root of the right side: 2.034852575 Break this problem into two subproblems by setting (x + -9.375) equal to 2.034852575 and -2.034852575.Subproblem 1
x + -9.375 = 2.034852575 Simplifying x + -9.375 = 2.034852575 Reorder the terms: -9.375 + x = 2.034852575 Solving -9.375 + x = 2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + x = 2.034852575 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + x = 2.034852575 + 9.375 x = 2.034852575 + 9.375 Combine like terms: 2.034852575 + 9.375 = 11.409852575 x = 11.409852575 Simplifying x = 11.409852575Subproblem 2
x + -9.375 = -2.034852575 Simplifying x + -9.375 = -2.034852575 Reorder the terms: -9.375 + x = -2.034852575 Solving -9.375 + x = -2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + x = -2.034852575 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + x = -2.034852575 + 9.375 x = -2.034852575 + 9.375 Combine like terms: -2.034852575 + 9.375 = 7.340147425 x = 7.340147425 Simplifying x = 7.340147425Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.409852575, 7.340147425}Solution
x = {11.409852575, 7.340147425}
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