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Simplifying 7x(7x + -1) = 8 Reorder the terms: 7x(-1 + 7x) = 8 (-1 * 7x + 7x * 7x) = 8 (-7x + 49x2) = 8 Solving -7x + 49x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -7x + 49x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -7x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.1632653061 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.1632653061' to each side of the equation. -0.1632653061 + -0.1428571429x + 0.1632653061 + x2 = 0 + 0.1632653061 Reorder the terms: -0.1632653061 + 0.1632653061 + -0.1428571429x + x2 = 0 + 0.1632653061 Combine like terms: -0.1632653061 + 0.1632653061 = 0.0000000000 0.0000000000 + -0.1428571429x + x2 = 0 + 0.1632653061 -0.1428571429x + x2 = 0 + 0.1632653061 Combine like terms: 0 + 0.1632653061 = 0.1632653061 -0.1428571429x + x2 = 0.1632653061 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 = 0.1632653061 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 0.1632653061 + 0.005102040819 Combine like terms: 0.1632653061 + 0.005102040819 = 0.168367346919 0.005102040819 + -0.1428571429x + x2 = 0.168367346919 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 0.168367346919 Calculate the square root of the right side: 0.410325903 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 0.410325903 and -0.410325903.Subproblem 1
x + -0.07142857145 = 0.410325903 Simplifying x + -0.07142857145 = 0.410325903 Reorder the terms: -0.07142857145 + x = 0.410325903 Solving -0.07142857145 + x = 0.410325903 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 = 0.410325903 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.410325903 + 0.07142857145 x = 0.410325903 + 0.07142857145 Combine like terms: 0.410325903 + 0.07142857145 = 0.48175447445 x = 0.48175447445 Simplifying x = 0.48175447445Subproblem 2
x + -0.07142857145 = -0.410325903 Simplifying x + -0.07142857145 = -0.410325903 Reorder the terms: -0.07142857145 + x = -0.410325903 Solving -0.07142857145 + x = -0.410325903 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 = -0.410325903 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.410325903 + 0.07142857145 x = -0.410325903 + 0.07142857145 Combine like terms: -0.410325903 + 0.07142857145 = -0.33889733155 x = -0.33889733155 Simplifying x = -0.33889733155Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.48175447445, -0.33889733155}
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