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Simplifying 4x2 + 72x = 6 Reorder the terms: 72x + 4x2 = 6 Solving 72x + 4x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 72x + 4x2 = 6 + -6 Combine like terms: 6 + -6 = 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 = 0.082951062 x = 0.082951062 Simplifying x = 0.082951062Subproblem 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 = -18.082951062 x = -18.082951062 Simplifying x = -18.082951062Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.082951062, -18.082951062}Solution
x = {0.082951062, -18.082951062}
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