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Simplifying 7x2 + 1x + -91 = 0 Reorder the terms: -91 + 1x + 7x2 = 0 Solving -91 + 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'. -13 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 0.1428571429x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 0.1428571429x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 0.1428571429x + x2 = 0 + 13 0.1428571429x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 0.1428571429x + x2 = 13 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 = 13 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 13 + 0.005102040819 Combine like terms: 13 + 0.005102040819 = 13.005102040819 0.005102040819 + 0.1428571429x + x2 = 13.005102040819 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 13.005102040819 Calculate the square root of the right side: 3.606258732 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 3.606258732 and -3.606258732.Subproblem 1
x + 0.07142857145 = 3.606258732 Simplifying x + 0.07142857145 = 3.606258732 Reorder the terms: 0.07142857145 + x = 3.606258732 Solving 0.07142857145 + x = 3.606258732 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 = 3.606258732 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 3.606258732 + -0.07142857145 x = 3.606258732 + -0.07142857145 Combine like terms: 3.606258732 + -0.07142857145 = 3.53483016055 x = 3.53483016055 Simplifying x = 3.53483016055Subproblem 2
x + 0.07142857145 = -3.606258732 Simplifying x + 0.07142857145 = -3.606258732 Reorder the terms: 0.07142857145 + x = -3.606258732 Solving 0.07142857145 + x = -3.606258732 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 = -3.606258732 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -3.606258732 + -0.07142857145 x = -3.606258732 + -0.07142857145 Combine like terms: -3.606258732 + -0.07142857145 = -3.67768730345 x = -3.67768730345 Simplifying x = -3.67768730345Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.53483016055, -3.67768730345}
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