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Simplifying 2x2 + 13x = -7 Reorder the terms: 13x + 2x2 = -7 Solving 13x + 2x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + 13x + 2x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 6.5x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 6.5x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 6.5x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 6.5x + x2 = 0 + -3.5 6.5x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 6.5x + x2 = -3.5 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 = -3.5 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -3.5 + 10.5625 Combine like terms: -3.5 + 10.5625 = 7.0625 10.5625 + 6.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + 3.25) equal to 2.657536453 and -2.657536453.Subproblem 1
x + 3.25 = 2.657536453 Simplifying x + 3.25 = 2.657536453 Reorder the terms: 3.25 + x = 2.657536453 Solving 3.25 + x = 2.657536453 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 = 2.657536453 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 2.657536453 + -3.25 x = 2.657536453 + -3.25 Combine like terms: 2.657536453 + -3.25 = -0.592463547 x = -0.592463547 Simplifying x = -0.592463547Subproblem 2
x + 3.25 = -2.657536453 Simplifying x + 3.25 = -2.657536453 Reorder the terms: 3.25 + x = -2.657536453 Solving 3.25 + x = -2.657536453 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 = -2.657536453 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -2.657536453 + -3.25 x = -2.657536453 + -3.25 Combine like terms: -2.657536453 + -3.25 = -5.907536453 x = -5.907536453 Simplifying x = -5.907536453Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.592463547, -5.907536453}
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