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Simplifying 7x2 + -1x + -12 = 0 Reorder the terms: -12 + -1x + 7x2 = 0 Solving -12 + -1x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.714285714 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + -0.1428571429x + 1.714285714 + x2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + -0.1428571429x + x2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + -0.1428571429x + x2 = 0 + 1.714285714 -0.1428571429x + x2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 -0.1428571429x + x2 = 1.714285714 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = 1.714285714 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 1.714285714 + 0.005102040819 Combine like terms: 1.714285714 + 0.005102040819 = 1.719387754819 0.005102040819 + -0.1428571429x + x2 = 1.719387754819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 1.719387754819 Calculate the square root of the right side: 1.311254268 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 1.311254268 and -1.311254268.Subproblem 1
x + -0.07142857145 = 1.311254268 Simplifying x + -0.07142857145 = 1.311254268 Reorder the terms: -0.07142857145 + x = 1.311254268 Solving -0.07142857145 + x = 1.311254268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 1.311254268 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 1.311254268 + 0.07142857145 x = 1.311254268 + 0.07142857145 Combine like terms: 1.311254268 + 0.07142857145 = 1.38268283945 x = 1.38268283945 Simplifying x = 1.38268283945Subproblem 2
x + -0.07142857145 = -1.311254268 Simplifying x + -0.07142857145 = -1.311254268 Reorder the terms: -0.07142857145 + x = -1.311254268 Solving -0.07142857145 + x = -1.311254268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -1.311254268 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -1.311254268 + 0.07142857145 x = -1.311254268 + 0.07142857145 Combine like terms: -1.311254268 + 0.07142857145 = -1.23982569655 x = -1.23982569655 Simplifying x = -1.23982569655Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.38268283945, -1.23982569655}
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