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Simplifying 2x2 + 18x + -160 = 0 Reorder the terms: -160 + 18x + 2x2 = 0 Solving -160 + 18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-80 + 9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-80 + 9x + x2)' equal to zero and attempt to solve: Simplifying -80 + 9x + x2 = 0 Solving -80 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 9x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 9x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 9x + x2 = 0 + 80 9x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 9x + x2 = 80 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 80 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 80 + 20.25 Combine like terms: 80 + 20.25 = 100.25 20.25 + 9x + x2 = 100.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + 4.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + 4.5 = 10.012492197 Simplifying x + 4.5 = 10.012492197 Reorder the terms: 4.5 + x = 10.012492197 Solving 4.5 + x = 10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 10.012492197 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 10.012492197 + -4.5 x = 10.012492197 + -4.5 Combine like terms: 10.012492197 + -4.5 = 5.512492197 x = 5.512492197 Simplifying x = 5.512492197Subproblem 2
x + 4.5 = -10.012492197 Simplifying x + 4.5 = -10.012492197 Reorder the terms: 4.5 + x = -10.012492197 Solving 4.5 + x = -10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -10.012492197 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -10.012492197 + -4.5 x = -10.012492197 + -4.5 Combine like terms: -10.012492197 + -4.5 = -14.512492197 x = -14.512492197 Simplifying x = -14.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.512492197, -14.512492197}Solution
x = {5.512492197, -14.512492197}
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