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Simplifying 2x2 + 13x = 12 Reorder the terms: 13x + 2x2 = 12 Solving 13x + 2x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 13x + 2x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + 6.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 6.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 6.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 6.5x + x2 = 0 + 6 6.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 6.5x + x2 = 6 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 = 6 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 6 + 10.5625 Combine like terms: 6 + 10.5625 = 16.5625 10.5625 + 6.5x + x2 = 16.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (x + 3.25) equal to 4.069705149 and -4.069705149.Subproblem 1
x + 3.25 = 4.069705149 Simplifying x + 3.25 = 4.069705149 Reorder the terms: 3.25 + x = 4.069705149 Solving 3.25 + x = 4.069705149 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 = 4.069705149 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 4.069705149 + -3.25 x = 4.069705149 + -3.25 Combine like terms: 4.069705149 + -3.25 = 0.819705149 x = 0.819705149 Simplifying x = 0.819705149Subproblem 2
x + 3.25 = -4.069705149 Simplifying x + 3.25 = -4.069705149 Reorder the terms: 3.25 + x = -4.069705149 Solving 3.25 + x = -4.069705149 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 = -4.069705149 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -4.069705149 + -3.25 x = -4.069705149 + -3.25 Combine like terms: -4.069705149 + -3.25 = -7.319705149 x = -7.319705149 Simplifying x = -7.319705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.819705149, -7.319705149}
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