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Simplifying 4x2 + -6 = 72x Reorder the terms: -6 + 4x2 = 72x Solving -6 + 4x2 = 72x Solving for variable 'x'. Reorder the terms: -6 + -72x + 4x2 = 72x + -72x Combine like terms: 72x + -72x = 0 -6 + -72x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -36x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -36x + 2x2)' equal to zero and attempt to solve: Simplifying -3 + -36x + 2x2 = 0 Solving -3 + -36x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -18x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -18x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -18x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -18x + x2 = 0 + 1.5 -18x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -18x + x2 = 1.5 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 1.5 + 81 Reorder the terms: 81 + -18x + x2 = 1.5 + 81 Combine like terms: 1.5 + 81 = 82.5 81 + -18x + x2 = 82.5 Factor a perfect square on the left side: (x + -9)(x + -9) = 82.5 Calculate the square root of the right side: 9.082951062 Break this problem into two subproblems by setting (x + -9) equal to 9.082951062 and -9.082951062.Subproblem 1
x + -9 = 9.082951062 Simplifying x + -9 = 9.082951062 Reorder the terms: -9 + x = 9.082951062 Solving -9 + x = 9.082951062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 9.082951062 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.082951062 + 9 x = 9.082951062 + 9 Combine like terms: 9.082951062 + 9 = 18.082951062 x = 18.082951062 Simplifying x = 18.082951062Subproblem 2
x + -9 = -9.082951062 Simplifying x + -9 = -9.082951062 Reorder the terms: -9 + x = -9.082951062 Solving -9 + x = -9.082951062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -9.082951062 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.082951062 + 9 x = -9.082951062 + 9 Combine like terms: -9.082951062 + 9 = -0.082951062 x = -0.082951062 Simplifying x = -0.082951062Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.082951062, -0.082951062}Solution
x = {18.082951062, -0.082951062}
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