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Simplifying 234x + 2106 + 141x = 9x2 + 72x Reorder the terms: 2106 + 234x + 141x = 9x2 + 72x Combine like terms: 234x + 141x = 375x 2106 + 375x = 9x2 + 72x Reorder the terms: 2106 + 375x = 72x + 9x2 Solving 2106 + 375x = 72x + 9x2 Solving for variable 'x'. Combine like terms: 375x + -72x = 303x 2106 + 303x + -9x2 = 72x + 9x2 + -72x + -9x2 Reorder the terms: 2106 + 303x + -9x2 = 72x + -72x + 9x2 + -9x2 Combine like terms: 72x + -72x = 0 2106 + 303x + -9x2 = 0 + 9x2 + -9x2 2106 + 303x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 2106 + 303x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(702 + 101x + -3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(702 + 101x + -3x2)' equal to zero and attempt to solve: Simplifying 702 + 101x + -3x2 = 0 Solving 702 + 101x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -234 + -33.66666667x + x2 = 0 Move the constant term to the right: Add '234' to each side of the equation. -234 + -33.66666667x + 234 + x2 = 0 + 234 Reorder the terms: -234 + 234 + -33.66666667x + x2 = 0 + 234 Combine like terms: -234 + 234 = 0 0 + -33.66666667x + x2 = 0 + 234 -33.66666667x + x2 = 0 + 234 Combine like terms: 0 + 234 = 234 -33.66666667x + x2 = 234 The x term is -33.66666667x. Take half its coefficient (-16.83333334). Square it (283.3611113) and add it to both sides. Add '283.3611113' to each side of the equation. -33.66666667x + 283.3611113 + x2 = 234 + 283.3611113 Reorder the terms: 283.3611113 + -33.66666667x + x2 = 234 + 283.3611113 Combine like terms: 234 + 283.3611113 = 517.3611113 283.3611113 + -33.66666667x + x2 = 517.3611113 Factor a perfect square on the left side: (x + -16.83333334)(x + -16.83333334) = 517.3611113 Calculate the square root of the right side: 22.745573444 Break this problem into two subproblems by setting (x + -16.83333334) equal to 22.745573444 and -22.745573444.Subproblem 1
x + -16.83333334 = 22.745573444 Simplifying x + -16.83333334 = 22.745573444 Reorder the terms: -16.83333334 + x = 22.745573444 Solving -16.83333334 + x = 22.745573444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.83333334' to each side of the equation. -16.83333334 + 16.83333334 + x = 22.745573444 + 16.83333334 Combine like terms: -16.83333334 + 16.83333334 = 0.00000000 0.00000000 + x = 22.745573444 + 16.83333334 x = 22.745573444 + 16.83333334 Combine like terms: 22.745573444 + 16.83333334 = 39.578906784 x = 39.578906784 Simplifying x = 39.578906784Subproblem 2
x + -16.83333334 = -22.745573444 Simplifying x + -16.83333334 = -22.745573444 Reorder the terms: -16.83333334 + x = -22.745573444 Solving -16.83333334 + x = -22.745573444 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.83333334' to each side of the equation. -16.83333334 + 16.83333334 + x = -22.745573444 + 16.83333334 Combine like terms: -16.83333334 + 16.83333334 = 0.00000000 0.00000000 + x = -22.745573444 + 16.83333334 x = -22.745573444 + 16.83333334 Combine like terms: -22.745573444 + 16.83333334 = -5.912240104 x = -5.912240104 Simplifying x = -5.912240104Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.578906784, -5.912240104}Solution
x = {39.578906784, -5.912240104}
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