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Simplifying 9x2 + -6x = 729 Reorder the terms: -6x + 9x2 = 729 Solving -6x + 9x2 = 729 Solving for variable 'x'. Reorder the terms: -729 + -6x + 9x2 = 729 + -729 Combine like terms: 729 + -729 = 0 -729 + -6x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-243 + -2x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-243 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying -243 + -2x + 3x2 = 0 Solving -243 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -81 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + -0.6666666667x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + -0.6666666667x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -0.6666666667x + x2 = 0 + 81 -0.6666666667x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 -0.6666666667x + x2 = 81 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = 81 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 81 + 0.1111111112 Combine like terms: 81 + 0.1111111112 = 81.1111111112 0.1111111112 + -0.6666666667x + x2 = 81.1111111112 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 81.1111111112 Calculate the square root of the right side: 9.006170724 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 9.006170724 and -9.006170724.Subproblem 1
x + -0.3333333334 = 9.006170724 Simplifying x + -0.3333333334 = 9.006170724 Reorder the terms: -0.3333333334 + x = 9.006170724 Solving -0.3333333334 + x = 9.006170724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = 9.006170724 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 9.006170724 + 0.3333333334 x = 9.006170724 + 0.3333333334 Combine like terms: 9.006170724 + 0.3333333334 = 9.3395040574 x = 9.3395040574 Simplifying x = 9.3395040574Subproblem 2
x + -0.3333333334 = -9.006170724 Simplifying x + -0.3333333334 = -9.006170724 Reorder the terms: -0.3333333334 + x = -9.006170724 Solving -0.3333333334 + x = -9.006170724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + x = -9.006170724 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -9.006170724 + 0.3333333334 x = -9.006170724 + 0.3333333334 Combine like terms: -9.006170724 + 0.3333333334 = -8.6728373906 x = -8.6728373906 Simplifying x = -8.6728373906Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.3395040574, -8.6728373906}Solution
x = {9.3395040574, -8.6728373906}
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