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Simplifying 2x2 + 72x + 36 = 0 Reorder the terms: 36 + 72x + 2x2 = 0 Solving 36 + 72x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(18 + 36x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + 36x + x2)' equal to zero and attempt to solve: Simplifying 18 + 36x + x2 = 0 Solving 18 + 36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 36x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 36x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 36x + x2 = 0 + -18 36x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 36x + x2 = -18 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = -18 + 324 Reorder the terms: 324 + 36x + x2 = -18 + 324 Combine like terms: -18 + 324 = 306 324 + 36x + x2 = 306 Factor a perfect square on the left side: (x + 18)(x + 18) = 306 Calculate the square root of the right side: 17.492855685 Break this problem into two subproblems by setting (x + 18) equal to 17.492855685 and -17.492855685.Subproblem 1
x + 18 = 17.492855685 Simplifying x + 18 = 17.492855685 Reorder the terms: 18 + x = 17.492855685 Solving 18 + x = 17.492855685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 17.492855685 + -18 Combine like terms: 18 + -18 = 0 0 + x = 17.492855685 + -18 x = 17.492855685 + -18 Combine like terms: 17.492855685 + -18 = -0.507144315 x = -0.507144315 Simplifying x = -0.507144315Subproblem 2
x + 18 = -17.492855685 Simplifying x + 18 = -17.492855685 Reorder the terms: 18 + x = -17.492855685 Solving 18 + x = -17.492855685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -17.492855685 + -18 Combine like terms: 18 + -18 = 0 0 + x = -17.492855685 + -18 x = -17.492855685 + -18 Combine like terms: -17.492855685 + -18 = -35.492855685 x = -35.492855685 Simplifying x = -35.492855685Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.507144315, -35.492855685}Solution
x = {-0.507144315, -35.492855685}
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