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Simplifying -2x2 + 52x = 300 Reorder the terms: 52x + -2x2 = 300 Solving 52x + -2x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 52x + -2x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 52x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-150 + 26x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-150 + 26x + -1x2)' equal to zero and attempt to solve: Simplifying -150 + 26x + -1x2 = 0 Solving -150 + 26x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 150 + -26x + x2 = 0 Move the constant term to the right: Add '-150' to each side of the equation. 150 + -26x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + -26x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -26x + x2 = 0 + -150 -26x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 -26x + x2 = -150 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -150 + 169 Reorder the terms: 169 + -26x + x2 = -150 + 169 Combine like terms: -150 + 169 = 19 169 + -26x + x2 = 19 Factor a perfect square on the left side: (x + -13)(x + -13) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -13) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -13 = 4.358898944 Simplifying x + -13 = 4.358898944 Reorder the terms: -13 + x = 4.358898944 Solving -13 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 4.358898944 + 13 Combine like terms: -13 + 13 = 0 0 + x = 4.358898944 + 13 x = 4.358898944 + 13 Combine like terms: 4.358898944 + 13 = 17.358898944 x = 17.358898944 Simplifying x = 17.358898944Subproblem 2
x + -13 = -4.358898944 Simplifying x + -13 = -4.358898944 Reorder the terms: -13 + x = -4.358898944 Solving -13 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -4.358898944 + 13 Combine like terms: -13 + 13 = 0 0 + x = -4.358898944 + 13 x = -4.358898944 + 13 Combine like terms: -4.358898944 + 13 = 8.641101056 x = 8.641101056 Simplifying x = 8.641101056Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.358898944, 8.641101056}Solution
x = {17.358898944, 8.641101056}
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