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Simplifying 2x2 + -58x + 160 = 0 Reorder the terms: 160 + -58x + 2x2 = 0 Solving 160 + -58x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(80 + -29x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(80 + -29x + x2)' equal to zero and attempt to solve: Simplifying 80 + -29x + x2 = 0 Solving 80 + -29x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + -29x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -29x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -29x + x2 = 0 + -80 -29x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -29x + x2 = -80 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -80 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -80 + 210.25 Combine like terms: -80 + 210.25 = 130.25 210.25 + -29x + x2 = 130.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (x + -14.5) equal to 11.412712211 and -11.412712211.Subproblem 1
x + -14.5 = 11.412712211 Simplifying x + -14.5 = 11.412712211 Reorder the terms: -14.5 + x = 11.412712211 Solving -14.5 + x = 11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 11.412712211 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 11.412712211 + 14.5 x = 11.412712211 + 14.5 Combine like terms: 11.412712211 + 14.5 = 25.912712211 x = 25.912712211 Simplifying x = 25.912712211Subproblem 2
x + -14.5 = -11.412712211 Simplifying x + -14.5 = -11.412712211 Reorder the terms: -14.5 + x = -11.412712211 Solving -14.5 + x = -11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -11.412712211 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -11.412712211 + 14.5 x = -11.412712211 + 14.5 Combine like terms: -11.412712211 + 14.5 = 3.087287789 x = 3.087287789 Simplifying x = 3.087287789Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.912712211, 3.087287789}Solution
x = {25.912712211, 3.087287789}
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