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Simplifying -1x(7x + -1) + 8(1 + 8) = 0 Reorder the terms: -1x(-1 + 7x) + 8(1 + 8) = 0 (-1 * -1x + 7x * -1x) + 8(1 + 8) = 0 (1x + -7x2) + 8(1 + 8) = 0 Combine like terms: 1 + 8 = 9 1x + -7x2 + 8(9) = 0 Multiply 8 * 9 1x + -7x2 + 72 = 0 Reorder the terms: 72 + 1x + -7x2 = 0 Solving 72 + 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'. -10.28571429 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '10.28571429' to each side of the equation. -10.28571429 + -0.1428571429x + 10.28571429 + x2 = 0 + 10.28571429 Reorder the terms: -10.28571429 + 10.28571429 + -0.1428571429x + x2 = 0 + 10.28571429 Combine like terms: -10.28571429 + 10.28571429 = 0.00000000 0.00000000 + -0.1428571429x + x2 = 0 + 10.28571429 -0.1428571429x + x2 = 0 + 10.28571429 Combine like terms: 0 + 10.28571429 = 10.28571429 -0.1428571429x + x2 = 10.28571429 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 = 10.28571429 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 10.28571429 + 0.005102040819 Combine like terms: 10.28571429 + 0.005102040819 = 10.290816330819 0.005102040819 + -0.1428571429x + x2 = 10.290816330819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 10.290816330819 Calculate the square root of the right side: 3.207930225 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 3.207930225 and -3.207930225.Subproblem 1
x + -0.07142857145 = 3.207930225 Simplifying x + -0.07142857145 = 3.207930225 Reorder the terms: -0.07142857145 + x = 3.207930225 Solving -0.07142857145 + x = 3.207930225 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 = 3.207930225 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 3.207930225 + 0.07142857145 x = 3.207930225 + 0.07142857145 Combine like terms: 3.207930225 + 0.07142857145 = 3.27935879645 x = 3.27935879645 Simplifying x = 3.27935879645Subproblem 2
x + -0.07142857145 = -3.207930225 Simplifying x + -0.07142857145 = -3.207930225 Reorder the terms: -0.07142857145 + x = -3.207930225 Solving -0.07142857145 + x = -3.207930225 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 = -3.207930225 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -3.207930225 + 0.07142857145 x = -3.207930225 + 0.07142857145 Combine like terms: -3.207930225 + 0.07142857145 = -3.13650165355 x = -3.13650165355 Simplifying x = -3.13650165355Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.27935879645, -3.13650165355}
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