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Simplifying 150x2 + 44056x + -8762491 = 0 Reorder the terms: -8762491 + 44056x + 150x2 = 0 Solving -8762491 + 44056x + 150x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 150 the coefficient of the squared term: Divide each side by '150'. -58416.60667 + 293.7066667x + x2 = 0 Move the constant term to the right: Add '58416.60667' to each side of the equation. -58416.60667 + 293.7066667x + 58416.60667 + x2 = 0 + 58416.60667 Reorder the terms: -58416.60667 + 58416.60667 + 293.7066667x + x2 = 0 + 58416.60667 Combine like terms: -58416.60667 + 58416.60667 = 0.00000 0.00000 + 293.7066667x + x2 = 0 + 58416.60667 293.7066667x + x2 = 0 + 58416.60667 Combine like terms: 0 + 58416.60667 = 58416.60667 293.7066667x + x2 = 58416.60667 The x term is 293.7066667x. Take half its coefficient (146.8533334). Square it (21565.90153) and add it to both sides. Add '21565.90153' to each side of the equation. 293.7066667x + 21565.90153 + x2 = 58416.60667 + 21565.90153 Reorder the terms: 21565.90153 + 293.7066667x + x2 = 58416.60667 + 21565.90153 Combine like terms: 58416.60667 + 21565.90153 = 79982.5082 21565.90153 + 293.7066667x + x2 = 79982.5082 Factor a perfect square on the left side: (x + 146.8533334)(x + 146.8533334) = 79982.5082 Calculate the square root of the right side: 282.811789358 Break this problem into two subproblems by setting (x + 146.8533334) equal to 282.811789358 and -282.811789358.Subproblem 1
x + 146.8533334 = 282.811789358 Simplifying x + 146.8533334 = 282.811789358 Reorder the terms: 146.8533334 + x = 282.811789358 Solving 146.8533334 + x = 282.811789358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-146.8533334' to each side of the equation. 146.8533334 + -146.8533334 + x = 282.811789358 + -146.8533334 Combine like terms: 146.8533334 + -146.8533334 = 0.0000000 0.0000000 + x = 282.811789358 + -146.8533334 x = 282.811789358 + -146.8533334 Combine like terms: 282.811789358 + -146.8533334 = 135.958455958 x = 135.958455958 Simplifying x = 135.958455958Subproblem 2
x + 146.8533334 = -282.811789358 Simplifying x + 146.8533334 = -282.811789358 Reorder the terms: 146.8533334 + x = -282.811789358 Solving 146.8533334 + x = -282.811789358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-146.8533334' to each side of the equation. 146.8533334 + -146.8533334 + x = -282.811789358 + -146.8533334 Combine like terms: 146.8533334 + -146.8533334 = 0.0000000 0.0000000 + x = -282.811789358 + -146.8533334 x = -282.811789358 + -146.8533334 Combine like terms: -282.811789358 + -146.8533334 = -429.665122758 x = -429.665122758 Simplifying x = -429.665122758Solution
The solution to the problem is based on the solutions from the subproblems. x = {135.958455958, -429.665122758}
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