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Simplifying 6x2 + 15x + -13 = 0 Reorder the terms: -13 + 15x + 6x2 = 0 Solving -13 + 15x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.166666667 + 2.5x + x2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + 2.5x + 2.166666667 + x2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + 2.5x + x2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + 2.5x + x2 = 0 + 2.166666667 2.5x + x2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 2.5x + x2 = 2.166666667 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 2.166666667 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 2.166666667 + 1.5625 Combine like terms: 2.166666667 + 1.5625 = 3.729166667 1.5625 + 2.5x + x2 = 3.729166667 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 3.729166667 Calculate the square root of the right side: 1.931105038 Break this problem into two subproblems by setting (x + 1.25) equal to 1.931105038 and -1.931105038.Subproblem 1
x + 1.25 = 1.931105038 Simplifying x + 1.25 = 1.931105038 Reorder the terms: 1.25 + x = 1.931105038 Solving 1.25 + x = 1.931105038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.931105038 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.931105038 + -1.25 x = 1.931105038 + -1.25 Combine like terms: 1.931105038 + -1.25 = 0.681105038 x = 0.681105038 Simplifying x = 0.681105038Subproblem 2
x + 1.25 = -1.931105038 Simplifying x + 1.25 = -1.931105038 Reorder the terms: 1.25 + x = -1.931105038 Solving 1.25 + x = -1.931105038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.931105038 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.931105038 + -1.25 x = -1.931105038 + -1.25 Combine like terms: -1.931105038 + -1.25 = -3.181105038 x = -3.181105038 Simplifying x = -3.181105038Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.681105038, -3.181105038}
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