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Simplifying 2x2 + 13x + -174 = 0 Reorder the terms: -174 + 13x + 2x2 = 0 Solving -174 + 13x + 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'. -87 + 6.5x + x2 = 0 Move the constant term to the right: Add '87' to each side of the equation. -87 + 6.5x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + 6.5x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + 6.5x + x2 = 0 + 87 6.5x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 6.5x + x2 = 87 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 87 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 87 + 10.5625 Combine like terms: 87 + 10.5625 = 97.5625 10.5625 + 6.5x + x2 = 97.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 97.5625 Calculate the square root of the right side: 9.877373133 Break this problem into two subproblems by setting (x + 3.25) equal to 9.877373133 and -9.877373133.Subproblem 1
x + 3.25 = 9.877373133 Simplifying x + 3.25 = 9.877373133 Reorder the terms: 3.25 + x = 9.877373133 Solving 3.25 + x = 9.877373133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 9.877373133 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 9.877373133 + -3.25 x = 9.877373133 + -3.25 Combine like terms: 9.877373133 + -3.25 = 6.627373133 x = 6.627373133 Simplifying x = 6.627373133Subproblem 2
x + 3.25 = -9.877373133 Simplifying x + 3.25 = -9.877373133 Reorder the terms: 3.25 + x = -9.877373133 Solving 3.25 + x = -9.877373133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -9.877373133 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -9.877373133 + -3.25 x = -9.877373133 + -3.25 Combine like terms: -9.877373133 + -3.25 = -13.127373133 x = -13.127373133 Simplifying x = -13.127373133Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.627373133, -13.127373133}
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