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Simplifying 6x2 + 45x + 18 = 0 Reorder the terms: 18 + 45x + 6x2 = 0 Solving 18 + 45x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + 15x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + 15x + 2x2)' equal to zero and attempt to solve: Simplifying 6 + 15x + 2x2 = 0 Solving 6 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 7.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 7.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 7.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7.5x + x2 = 0 + -3 7.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 7.5x + x2 = -3 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = -3 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = -3 + 14.0625 Combine like terms: -3 + 14.0625 = 11.0625 14.0625 + 7.5x + x2 = 11.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (x + 3.75) equal to 3.326033674 and -3.326033674.Subproblem 1
x + 3.75 = 3.326033674 Simplifying x + 3.75 = 3.326033674 Reorder the terms: 3.75 + x = 3.326033674 Solving 3.75 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 3.326033674 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 3.326033674 + -3.75 x = 3.326033674 + -3.75 Combine like terms: 3.326033674 + -3.75 = -0.423966326 x = -0.423966326 Simplifying x = -0.423966326Subproblem 2
x + 3.75 = -3.326033674 Simplifying x + 3.75 = -3.326033674 Reorder the terms: 3.75 + x = -3.326033674 Solving 3.75 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -3.326033674 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -3.326033674 + -3.75 x = -3.326033674 + -3.75 Combine like terms: -3.326033674 + -3.75 = -7.076033674 x = -7.076033674 Simplifying x = -7.076033674Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.423966326, -7.076033674}Solution
x = {-0.423966326, -7.076033674}
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