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Simplifying 2x2 + 20x + -24 = 0 Reorder the terms: -24 + 20x + 2x2 = 0 Solving -24 + 20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 10x + x2)' equal to zero and attempt to solve: Simplifying -12 + 10x + x2 = 0 Solving -12 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 10x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 10x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 10x + x2 = 0 + 12 10x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 10x + x2 = 12 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 12 + 25 Reorder the terms: 25 + 10x + x2 = 12 + 25 Combine like terms: 12 + 25 = 37 25 + 10x + x2 = 37 Factor a perfect square on the left side: (x + 5)(x + 5) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + 5) equal to 6.08276253 and -6.08276253.Subproblem 1
x + 5 = 6.08276253 Simplifying x + 5 = 6.08276253 Reorder the terms: 5 + x = 6.08276253 Solving 5 + x = 6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 6.08276253 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.08276253 + -5 x = 6.08276253 + -5 Combine like terms: 6.08276253 + -5 = 1.08276253 x = 1.08276253 Simplifying x = 1.08276253Subproblem 2
x + 5 = -6.08276253 Simplifying x + 5 = -6.08276253 Reorder the terms: 5 + x = -6.08276253 Solving 5 + x = -6.08276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -6.08276253 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.08276253 + -5 x = -6.08276253 + -5 Combine like terms: -6.08276253 + -5 = -11.08276253 x = -11.08276253 Simplifying x = -11.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.08276253, -11.08276253}Solution
x = {1.08276253, -11.08276253}
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