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Simplifying 2x2 + 13x = 186 Reorder the terms: 13x + 2x2 = 186 Solving 13x + 2x2 = 186 Solving for variable 'x'. Reorder the terms: -186 + 13x + 2x2 = 186 + -186 Combine like terms: 186 + -186 = 0 -186 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -93 + 6.5x + x2 = 0 Move the constant term to the right: Add '93' to each side of the equation. -93 + 6.5x + 93 + x2 = 0 + 93 Reorder the terms: -93 + 93 + 6.5x + x2 = 0 + 93 Combine like terms: -93 + 93 = 0 0 + 6.5x + x2 = 0 + 93 6.5x + x2 = 0 + 93 Combine like terms: 0 + 93 = 93 6.5x + x2 = 93 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 = 93 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 93 + 10.5625 Combine like terms: 93 + 10.5625 = 103.5625 10.5625 + 6.5x + x2 = 103.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 103.5625 Calculate the square root of the right side: 10.176566219 Break this problem into two subproblems by setting (x + 3.25) equal to 10.176566219 and -10.176566219.Subproblem 1
x + 3.25 = 10.176566219 Simplifying x + 3.25 = 10.176566219 Reorder the terms: 3.25 + x = 10.176566219 Solving 3.25 + x = 10.176566219 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 = 10.176566219 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 10.176566219 + -3.25 x = 10.176566219 + -3.25 Combine like terms: 10.176566219 + -3.25 = 6.926566219 x = 6.926566219 Simplifying x = 6.926566219Subproblem 2
x + 3.25 = -10.176566219 Simplifying x + 3.25 = -10.176566219 Reorder the terms: 3.25 + x = -10.176566219 Solving 3.25 + x = -10.176566219 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 = -10.176566219 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -10.176566219 + -3.25 x = -10.176566219 + -3.25 Combine like terms: -10.176566219 + -3.25 = -13.426566219 x = -13.426566219 Simplifying x = -13.426566219Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.926566219, -13.426566219}
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