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Simplifying (7x + -1) * x = 13 Reorder the terms: (-1 + 7x) * x = 13 Reorder the terms for easier multiplication: x(-1 + 7x) = 13 (-1 * x + 7x * x) = 13 (-1x + 7x2) = 13 Solving -1x + 7x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -1x + 7x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -1x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.857142857 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '1.857142857' to each side of the equation. -1.857142857 + -0.1428571429x + 1.857142857 + x2 = 0 + 1.857142857 Reorder the terms: -1.857142857 + 1.857142857 + -0.1428571429x + x2 = 0 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + -0.1428571429x + x2 = 0 + 1.857142857 -0.1428571429x + x2 = 0 + 1.857142857 Combine like terms: 0 + 1.857142857 = 1.857142857 -0.1428571429x + x2 = 1.857142857 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 = 1.857142857 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 1.857142857 + 0.005102040819 Combine like terms: 1.857142857 + 0.005102040819 = 1.862244897819 0.005102040819 + -0.1428571429x + x2 = 1.862244897819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 1.862244897819 Calculate the square root of the right side: 1.364640941 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 1.364640941 and -1.364640941.Subproblem 1
x + -0.07142857145 = 1.364640941 Simplifying x + -0.07142857145 = 1.364640941 Reorder the terms: -0.07142857145 + x = 1.364640941 Solving -0.07142857145 + x = 1.364640941 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 = 1.364640941 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 1.364640941 + 0.07142857145 x = 1.364640941 + 0.07142857145 Combine like terms: 1.364640941 + 0.07142857145 = 1.43606951245 x = 1.43606951245 Simplifying x = 1.43606951245Subproblem 2
x + -0.07142857145 = -1.364640941 Simplifying x + -0.07142857145 = -1.364640941 Reorder the terms: -0.07142857145 + x = -1.364640941 Solving -0.07142857145 + x = -1.364640941 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 = -1.364640941 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -1.364640941 + 0.07142857145 x = -1.364640941 + 0.07142857145 Combine like terms: -1.364640941 + 0.07142857145 = -1.29321236955 x = -1.29321236955 Simplifying x = -1.29321236955Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.43606951245, -1.29321236955}
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