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Simplifying 234x2 + -12x + -24 = 0 Reorder the terms: -24 + -12x + 234x2 = 0 Solving -24 + -12x + 234x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-4 + -2x + 39x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-4 + -2x + 39x2)' equal to zero and attempt to solve: Simplifying -4 + -2x + 39x2 = 0 Solving -4 + -2x + 39x2 = 0 Begin completing the square. Divide all terms by 39 the coefficient of the squared term: Divide each side by '39'. -0.1025641026 + -0.05128205128x + x2 = 0 Move the constant term to the right: Add '0.1025641026' to each side of the equation. -0.1025641026 + -0.05128205128x + 0.1025641026 + x2 = 0 + 0.1025641026 Reorder the terms: -0.1025641026 + 0.1025641026 + -0.05128205128x + x2 = 0 + 0.1025641026 Combine like terms: -0.1025641026 + 0.1025641026 = 0.0000000000 0.0000000000 + -0.05128205128x + x2 = 0 + 0.1025641026 -0.05128205128x + x2 = 0 + 0.1025641026 Combine like terms: 0 + 0.1025641026 = 0.1025641026 -0.05128205128x + x2 = 0.1025641026 The x term is -0.05128205128x. Take half its coefficient (-0.02564102564). Square it (0.0006574621959) and add it to both sides. Add '0.0006574621959' to each side of the equation. -0.05128205128x + 0.0006574621959 + x2 = 0.1025641026 + 0.0006574621959 Reorder the terms: 0.0006574621959 + -0.05128205128x + x2 = 0.1025641026 + 0.0006574621959 Combine like terms: 0.1025641026 + 0.0006574621959 = 0.1032215647959 0.0006574621959 + -0.05128205128x + x2 = 0.1032215647959 Factor a perfect square on the left side: (x + -0.02564102564)(x + -0.02564102564) = 0.1032215647959 Calculate the square root of the right side: 0.32128113 Break this problem into two subproblems by setting (x + -0.02564102564) equal to 0.32128113 and -0.32128113.Subproblem 1
x + -0.02564102564 = 0.32128113 Simplifying x + -0.02564102564 = 0.32128113 Reorder the terms: -0.02564102564 + x = 0.32128113 Solving -0.02564102564 + x = 0.32128113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02564102564' to each side of the equation. -0.02564102564 + 0.02564102564 + x = 0.32128113 + 0.02564102564 Combine like terms: -0.02564102564 + 0.02564102564 = 0.00000000000 0.00000000000 + x = 0.32128113 + 0.02564102564 x = 0.32128113 + 0.02564102564 Combine like terms: 0.32128113 + 0.02564102564 = 0.34692215564 x = 0.34692215564 Simplifying x = 0.34692215564Subproblem 2
x + -0.02564102564 = -0.32128113 Simplifying x + -0.02564102564 = -0.32128113 Reorder the terms: -0.02564102564 + x = -0.32128113 Solving -0.02564102564 + x = -0.32128113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02564102564' to each side of the equation. -0.02564102564 + 0.02564102564 + x = -0.32128113 + 0.02564102564 Combine like terms: -0.02564102564 + 0.02564102564 = 0.00000000000 0.00000000000 + x = -0.32128113 + 0.02564102564 x = -0.32128113 + 0.02564102564 Combine like terms: -0.32128113 + 0.02564102564 = -0.29564010436 x = -0.29564010436 Simplifying x = -0.29564010436Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.34692215564, -0.29564010436}Solution
x = {0.34692215564, -0.29564010436}
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