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Simplifying (x + 10)(14x + -58) = 9x Reorder the terms: (10 + x)(14x + -58) = 9x Reorder the terms: (10 + x)(-58 + 14x) = 9x Multiply (10 + x) * (-58 + 14x) (10(-58 + 14x) + x(-58 + 14x)) = 9x ((-58 * 10 + 14x * 10) + x(-58 + 14x)) = 9x ((-580 + 140x) + x(-58 + 14x)) = 9x (-580 + 140x + (-58 * x + 14x * x)) = 9x (-580 + 140x + (-58x + 14x2)) = 9x Combine like terms: 140x + -58x = 82x (-580 + 82x + 14x2) = 9x Solving -580 + 82x + 14x2 = 9x Solving for variable 'x'. Reorder the terms: -580 + 82x + -9x + 14x2 = 9x + -9x Combine like terms: 82x + -9x = 73x -580 + 73x + 14x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -580 + 73x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -41.42857143 + 5.214285714x + x2 = 0 Move the constant term to the right: Add '41.42857143' to each side of the equation. -41.42857143 + 5.214285714x + 41.42857143 + x2 = 0 + 41.42857143 Reorder the terms: -41.42857143 + 41.42857143 + 5.214285714x + x2 = 0 + 41.42857143 Combine like terms: -41.42857143 + 41.42857143 = 0.00000000 0.00000000 + 5.214285714x + x2 = 0 + 41.42857143 5.214285714x + x2 = 0 + 41.42857143 Combine like terms: 0 + 41.42857143 = 41.42857143 5.214285714x + x2 = 41.42857143 The x term is 5.214285714x. Take half its coefficient (2.607142857). Square it (6.797193877) and add it to both sides. Add '6.797193877' to each side of the equation. 5.214285714x + 6.797193877 + x2 = 41.42857143 + 6.797193877 Reorder the terms: 6.797193877 + 5.214285714x + x2 = 41.42857143 + 6.797193877 Combine like terms: 41.42857143 + 6.797193877 = 48.225765307 6.797193877 + 5.214285714x + x2 = 48.225765307 Factor a perfect square on the left side: (x + 2.607142857)(x + 2.607142857) = 48.225765307 Calculate the square root of the right side: 6.944477324 Break this problem into two subproblems by setting (x + 2.607142857) equal to 6.944477324 and -6.944477324.Subproblem 1
x + 2.607142857 = 6.944477324 Simplifying x + 2.607142857 = 6.944477324 Reorder the terms: 2.607142857 + x = 6.944477324 Solving 2.607142857 + x = 6.944477324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.607142857' to each side of the equation. 2.607142857 + -2.607142857 + x = 6.944477324 + -2.607142857 Combine like terms: 2.607142857 + -2.607142857 = 0.000000000 0.000000000 + x = 6.944477324 + -2.607142857 x = 6.944477324 + -2.607142857 Combine like terms: 6.944477324 + -2.607142857 = 4.337334467 x = 4.337334467 Simplifying x = 4.337334467Subproblem 2
x + 2.607142857 = -6.944477324 Simplifying x + 2.607142857 = -6.944477324 Reorder the terms: 2.607142857 + x = -6.944477324 Solving 2.607142857 + x = -6.944477324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.607142857' to each side of the equation. 2.607142857 + -2.607142857 + x = -6.944477324 + -2.607142857 Combine like terms: 2.607142857 + -2.607142857 = 0.000000000 0.000000000 + x = -6.944477324 + -2.607142857 x = -6.944477324 + -2.607142857 Combine like terms: -6.944477324 + -2.607142857 = -9.551620181 x = -9.551620181 Simplifying x = -9.551620181Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.337334467, -9.551620181}
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