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Simplifying 2x2 + -60 = 24x Reorder the terms: -60 + 2x2 = 24x Solving -60 + 2x2 = 24x Solving for variable 'x'. Reorder the terms: -60 + -24x + 2x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -60 + -24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + -12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + -12x + x2)' equal to zero and attempt to solve: Simplifying -30 + -12x + x2 = 0 Solving -30 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -12x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -12x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -12x + x2 = 0 + 30 -12x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -12x + x2 = 30 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 = 30 + 36 Reorder the terms: 36 + -12x + x2 = 30 + 36 Combine like terms: 30 + 36 = 66 36 + -12x + x2 = 66 Factor a perfect square on the left side: (x + -6)(x + -6) = 66 Calculate the square root of the right side: 8.124038405 Break this problem into two subproblems by setting (x + -6) equal to 8.124038405 and -8.124038405.Subproblem 1
x + -6 = 8.124038405 Simplifying x + -6 = 8.124038405 Reorder the terms: -6 + x = 8.124038405 Solving -6 + x = 8.124038405 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 = 8.124038405 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.124038405 + 6 x = 8.124038405 + 6 Combine like terms: 8.124038405 + 6 = 14.124038405 x = 14.124038405 Simplifying x = 14.124038405Subproblem 2
x + -6 = -8.124038405 Simplifying x + -6 = -8.124038405 Reorder the terms: -6 + x = -8.124038405 Solving -6 + x = -8.124038405 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 = -8.124038405 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.124038405 + 6 x = -8.124038405 + 6 Combine like terms: -8.124038405 + 6 = -2.124038405 x = -2.124038405 Simplifying x = -2.124038405Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.124038405, -2.124038405}Solution
x = {14.124038405, -2.124038405}
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