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Simplifying 6(x2 + 24x + 18) = 0 Reorder the terms: 6(18 + 24x + x2) = 0 (18 * 6 + 24x * 6 + x2 * 6) = 0 (108 + 144x + 6x2) = 0 Solving 108 + 144x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(18 + 24x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(18 + 24x + x2)' equal to zero and attempt to solve: Simplifying 18 + 24x + x2 = 0 Solving 18 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 24x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 24x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 24x + x2 = 0 + -18 24x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 24x + x2 = -18 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -18 + 144 Reorder the terms: 144 + 24x + x2 = -18 + 144 Combine like terms: -18 + 144 = 126 144 + 24x + x2 = 126 Factor a perfect square on the left side: (x + 12)(x + 12) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x + 12) equal to 11.22497216 and -11.22497216.Subproblem 1
x + 12 = 11.22497216 Simplifying x + 12 = 11.22497216 Reorder the terms: 12 + x = 11.22497216 Solving 12 + x = 11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 11.22497216 + -12 Combine like terms: 12 + -12 = 0 0 + x = 11.22497216 + -12 x = 11.22497216 + -12 Combine like terms: 11.22497216 + -12 = -0.77502784 x = -0.77502784 Simplifying x = -0.77502784Subproblem 2
x + 12 = -11.22497216 Simplifying x + 12 = -11.22497216 Reorder the terms: 12 + x = -11.22497216 Solving 12 + x = -11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -11.22497216 + -12 Combine like terms: 12 + -12 = 0 0 + x = -11.22497216 + -12 x = -11.22497216 + -12 Combine like terms: -11.22497216 + -12 = -23.22497216 x = -23.22497216 Simplifying x = -23.22497216Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.77502784, -23.22497216}Solution
x = {-0.77502784, -23.22497216}
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