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Simplifying 2x2 + -14x + -176 = 0 Reorder the terms: -176 + -14x + 2x2 = 0 Solving -176 + -14x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-88 + -7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-88 + -7x + x2)' equal to zero and attempt to solve: Simplifying -88 + -7x + x2 = 0 Solving -88 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + -7x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + -7x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + -7x + x2 = 0 + 88 -7x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 -7x + x2 = 88 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 88 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 88 + 12.25 Combine like terms: 88 + 12.25 = 100.25 12.25 + -7x + x2 = 100.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + -3.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + -3.5 = 10.012492197 Simplifying x + -3.5 = 10.012492197 Reorder the terms: -3.5 + x = 10.012492197 Solving -3.5 + x = 10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 10.012492197 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 10.012492197 + 3.5 x = 10.012492197 + 3.5 Combine like terms: 10.012492197 + 3.5 = 13.512492197 x = 13.512492197 Simplifying x = 13.512492197Subproblem 2
x + -3.5 = -10.012492197 Simplifying x + -3.5 = -10.012492197 Reorder the terms: -3.5 + x = -10.012492197 Solving -3.5 + x = -10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -10.012492197 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -10.012492197 + 3.5 x = -10.012492197 + 3.5 Combine like terms: -10.012492197 + 3.5 = -6.512492197 x = -6.512492197 Simplifying x = -6.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.512492197, -6.512492197}Solution
x = {13.512492197, -6.512492197}
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