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Simplifying 2x2 + 24x + -540 = 0 Reorder the terms: -540 + 24x + 2x2 = 0 Solving -540 + 24x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-270 + 12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-270 + 12x + x2)' equal to zero and attempt to solve: Simplifying -270 + 12x + x2 = 0 Solving -270 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + 12x + 270 + x2 = 0 + 270 Reorder the terms: -270 + 270 + 12x + x2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + 12x + x2 = 0 + 270 12x + x2 = 0 + 270 Combine like terms: 0 + 270 = 270 12x + x2 = 270 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 270 + 36 Reorder the terms: 36 + 12x + x2 = 270 + 36 Combine like terms: 270 + 36 = 306 36 + 12x + x2 = 306 Factor a perfect square on the left side: (x + 6)(x + 6) = 306 Calculate the square root of the right side: 17.492855685 Break this problem into two subproblems by setting (x + 6) equal to 17.492855685 and -17.492855685.Subproblem 1
x + 6 = 17.492855685 Simplifying x + 6 = 17.492855685 Reorder the terms: 6 + x = 17.492855685 Solving 6 + x = 17.492855685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 17.492855685 + -6 Combine like terms: 6 + -6 = 0 0 + x = 17.492855685 + -6 x = 17.492855685 + -6 Combine like terms: 17.492855685 + -6 = 11.492855685 x = 11.492855685 Simplifying x = 11.492855685Subproblem 2
x + 6 = -17.492855685 Simplifying x + 6 = -17.492855685 Reorder the terms: 6 + x = -17.492855685 Solving 6 + x = -17.492855685 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -17.492855685 + -6 Combine like terms: 6 + -6 = 0 0 + x = -17.492855685 + -6 x = -17.492855685 + -6 Combine like terms: -17.492855685 + -6 = -23.492855685 x = -23.492855685 Simplifying x = -23.492855685Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.492855685, -23.492855685}Solution
x = {11.492855685, -23.492855685}
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