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Simplifying 2x2 + 13x + -326 = 0 Reorder the terms: -326 + 13x + 2x2 = 0 Solving -326 + 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'. -163 + 6.5x + x2 = 0 Move the constant term to the right: Add '163' to each side of the equation. -163 + 6.5x + 163 + x2 = 0 + 163 Reorder the terms: -163 + 163 + 6.5x + x2 = 0 + 163 Combine like terms: -163 + 163 = 0 0 + 6.5x + x2 = 0 + 163 6.5x + x2 = 0 + 163 Combine like terms: 0 + 163 = 163 6.5x + x2 = 163 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 = 163 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 163 + 10.5625 Combine like terms: 163 + 10.5625 = 173.5625 10.5625 + 6.5x + x2 = 173.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 173.5625 Calculate the square root of the right side: 13.174312126 Break this problem into two subproblems by setting (x + 3.25) equal to 13.174312126 and -13.174312126.Subproblem 1
x + 3.25 = 13.174312126 Simplifying x + 3.25 = 13.174312126 Reorder the terms: 3.25 + x = 13.174312126 Solving 3.25 + x = 13.174312126 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 = 13.174312126 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 13.174312126 + -3.25 x = 13.174312126 + -3.25 Combine like terms: 13.174312126 + -3.25 = 9.924312126 x = 9.924312126 Simplifying x = 9.924312126Subproblem 2
x + 3.25 = -13.174312126 Simplifying x + 3.25 = -13.174312126 Reorder the terms: 3.25 + x = -13.174312126 Solving 3.25 + x = -13.174312126 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 = -13.174312126 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -13.174312126 + -3.25 x = -13.174312126 + -3.25 Combine like terms: -13.174312126 + -3.25 = -16.424312126 x = -16.424312126 Simplifying x = -16.424312126Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.924312126, -16.424312126}
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