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Simplifying 2x2 + 24x = 176 Reorder the terms: 24x + 2x2 = 176 Solving 24x + 2x2 = 176 Solving for variable 'x'. Reorder the terms: -176 + 24x + 2x2 = 176 + -176 Combine like terms: 176 + -176 = 0 -176 + 24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-88 + 12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-88 + 12x + x2)' equal to zero and attempt to solve: Simplifying -88 + 12x + x2 = 0 Solving -88 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 12x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + 12x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 12x + x2 = 0 + 88 12x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 12x + x2 = 88 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 = 88 + 36 Reorder the terms: 36 + 12x + x2 = 88 + 36 Combine like terms: 88 + 36 = 124 36 + 12x + x2 = 124 Factor a perfect square on the left side: (x + 6)(x + 6) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (x + 6) equal to 11.135528726 and -11.135528726.Subproblem 1
x + 6 = 11.135528726 Simplifying x + 6 = 11.135528726 Reorder the terms: 6 + x = 11.135528726 Solving 6 + x = 11.135528726 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 = 11.135528726 + -6 Combine like terms: 6 + -6 = 0 0 + x = 11.135528726 + -6 x = 11.135528726 + -6 Combine like terms: 11.135528726 + -6 = 5.135528726 x = 5.135528726 Simplifying x = 5.135528726Subproblem 2
x + 6 = -11.135528726 Simplifying x + 6 = -11.135528726 Reorder the terms: 6 + x = -11.135528726 Solving 6 + x = -11.135528726 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 = -11.135528726 + -6 Combine like terms: 6 + -6 = 0 0 + x = -11.135528726 + -6 x = -11.135528726 + -6 Combine like terms: -11.135528726 + -6 = -17.135528726 x = -17.135528726 Simplifying x = -17.135528726Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.135528726, -17.135528726}Solution
x = {5.135528726, -17.135528726}
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