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Simplifying 2x2 + -58x + 159 = 0 Reorder the terms: 159 + -58x + 2x2 = 0 Solving 159 + -58x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 79.5 + -29x + x2 = 0 Move the constant term to the right: Add '-79.5' to each side of the equation. 79.5 + -29x + -79.5 + x2 = 0 + -79.5 Reorder the terms: 79.5 + -79.5 + -29x + x2 = 0 + -79.5 Combine like terms: 79.5 + -79.5 = 0.0 0.0 + -29x + x2 = 0 + -79.5 -29x + x2 = 0 + -79.5 Combine like terms: 0 + -79.5 = -79.5 -29x + x2 = -79.5 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 = -79.5 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -79.5 + 210.25 Combine like terms: -79.5 + 210.25 = 130.75 210.25 + -29x + x2 = 130.75 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 130.75 Calculate the square root of the right side: 11.434596626 Break this problem into two subproblems by setting (x + -14.5) equal to 11.434596626 and -11.434596626.Subproblem 1
x + -14.5 = 11.434596626 Simplifying x + -14.5 = 11.434596626 Reorder the terms: -14.5 + x = 11.434596626 Solving -14.5 + x = 11.434596626 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 = 11.434596626 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 11.434596626 + 14.5 x = 11.434596626 + 14.5 Combine like terms: 11.434596626 + 14.5 = 25.934596626 x = 25.934596626 Simplifying x = 25.934596626Subproblem 2
x + -14.5 = -11.434596626 Simplifying x + -14.5 = -11.434596626 Reorder the terms: -14.5 + x = -11.434596626 Solving -14.5 + x = -11.434596626 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 = -11.434596626 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -11.434596626 + 14.5 x = -11.434596626 + 14.5 Combine like terms: -11.434596626 + 14.5 = 3.065403374 x = 3.065403374 Simplifying x = 3.065403374Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.934596626, 3.065403374}
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