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Simplifying 6x(x + -6) = -3(x + 3) Reorder the terms: 6x(-6 + x) = -3(x + 3) (-6 * 6x + x * 6x) = -3(x + 3) (-36x + 6x2) = -3(x + 3) Reorder the terms: -36x + 6x2 = -3(3 + x) -36x + 6x2 = (3 * -3 + x * -3) -36x + 6x2 = (-9 + -3x) Solving -36x + 6x2 = -9 + -3x Solving for variable 'x'. Reorder the terms: 9 + -36x + 3x + 6x2 = -9 + -3x + 9 + 3x Combine like terms: -36x + 3x = -33x 9 + -33x + 6x2 = -9 + -3x + 9 + 3x Reorder the terms: 9 + -33x + 6x2 = -9 + 9 + -3x + 3x Combine like terms: -9 + 9 = 0 9 + -33x + 6x2 = 0 + -3x + 3x 9 + -33x + 6x2 = -3x + 3x Combine like terms: -3x + 3x = 0 9 + -33x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -11x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -11x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + -11x + 2x2 = 0 Solving 3 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -5.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -5.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -5.5x + x2 = 0 + -1.5 -5.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -5.5x + x2 = -1.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -1.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -1.5 + 7.5625 Combine like terms: -1.5 + 7.5625 = 6.0625 7.5625 + -5.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + -2.75) equal to 2.46221445 and -2.46221445.Subproblem 1
x + -2.75 = 2.46221445 Simplifying x + -2.75 = 2.46221445 Reorder the terms: -2.75 + x = 2.46221445 Solving -2.75 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.46221445 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.46221445 + 2.75 x = 2.46221445 + 2.75 Combine like terms: 2.46221445 + 2.75 = 5.21221445 x = 5.21221445 Simplifying x = 5.21221445Subproblem 2
x + -2.75 = -2.46221445 Simplifying x + -2.75 = -2.46221445 Reorder the terms: -2.75 + x = -2.46221445 Solving -2.75 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.46221445 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.46221445 + 2.75 x = -2.46221445 + 2.75 Combine like terms: -2.46221445 + 2.75 = 0.28778555 x = 0.28778555 Simplifying x = 0.28778555Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.21221445, 0.28778555}Solution
x = {5.21221445, 0.28778555}
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