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Simplifying 9x(7x + -1) = 2 Reorder the terms: 9x(-1 + 7x) = 2 (-1 * 9x + 7x * 9x) = 2 (-9x + 63x2) = 2 Solving -9x + 63x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -9x + 63x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -9x + 63x2 = 0 Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -0.03174603175 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.03174603175' to each side of the equation. -0.03174603175 + -0.1428571429x + 0.03174603175 + x2 = 0 + 0.03174603175 Reorder the terms: -0.03174603175 + 0.03174603175 + -0.1428571429x + x2 = 0 + 0.03174603175 Combine like terms: -0.03174603175 + 0.03174603175 = 0.00000000000 0.00000000000 + -0.1428571429x + x2 = 0 + 0.03174603175 -0.1428571429x + x2 = 0 + 0.03174603175 Combine like terms: 0 + 0.03174603175 = 0.03174603175 -0.1428571429x + x2 = 0.03174603175 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 = 0.03174603175 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 0.03174603175 + 0.005102040819 Combine like terms: 0.03174603175 + 0.005102040819 = 0.036848072569 0.005102040819 + -0.1428571429x + x2 = 0.036848072569 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 0.036848072569 Calculate the square root of the right side: 0.191958518 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 0.191958518 and -0.191958518.Subproblem 1
x + -0.07142857145 = 0.191958518 Simplifying x + -0.07142857145 = 0.191958518 Reorder the terms: -0.07142857145 + x = 0.191958518 Solving -0.07142857145 + x = 0.191958518 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 = 0.191958518 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.191958518 + 0.07142857145 x = 0.191958518 + 0.07142857145 Combine like terms: 0.191958518 + 0.07142857145 = 0.26338708945 x = 0.26338708945 Simplifying x = 0.26338708945Subproblem 2
x + -0.07142857145 = -0.191958518 Simplifying x + -0.07142857145 = -0.191958518 Reorder the terms: -0.07142857145 + x = -0.191958518 Solving -0.07142857145 + x = -0.191958518 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 = -0.191958518 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.191958518 + 0.07142857145 x = -0.191958518 + 0.07142857145 Combine like terms: -0.191958518 + 0.07142857145 = -0.12052994655 x = -0.12052994655 Simplifying x = -0.12052994655Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.26338708945, -0.12052994655}
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