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Simplifying -7x(x + 9) = 8x + -6 Reorder the terms: -7x(9 + x) = 8x + -6 (9 * -7x + x * -7x) = 8x + -6 (-63x + -7x2) = 8x + -6 Reorder the terms: -63x + -7x2 = -6 + 8x Solving -63x + -7x2 = -6 + 8x Solving for variable 'x'. Reorder the terms: 6 + -63x + -8x + -7x2 = -6 + 8x + 6 + -8x Combine like terms: -63x + -8x = -71x 6 + -71x + -7x2 = -6 + 8x + 6 + -8x Reorder the terms: 6 + -71x + -7x2 = -6 + 6 + 8x + -8x Combine like terms: -6 + 6 = 0 6 + -71x + -7x2 = 0 + 8x + -8x 6 + -71x + -7x2 = 8x + -8x Combine like terms: 8x + -8x = 0 6 + -71x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -0.8571428571 + 10.14285714x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 10.14285714x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 10.14285714x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 10.14285714x + x2 = 0 + 0.8571428571 10.14285714x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 10.14285714x + x2 = 0.8571428571 The x term is 10.14285714x. Take half its coefficient (5.07142857). Square it (25.71938774) and add it to both sides. Add '25.71938774' to each side of the equation. 10.14285714x + 25.71938774 + x2 = 0.8571428571 + 25.71938774 Reorder the terms: 25.71938774 + 10.14285714x + x2 = 0.8571428571 + 25.71938774 Combine like terms: 0.8571428571 + 25.71938774 = 26.5765305971 25.71938774 + 10.14285714x + x2 = 26.5765305971 Factor a perfect square on the left side: (x + 5.07142857)(x + 5.07142857) = 26.5765305971 Calculate the square root of the right side: 5.15524302 Break this problem into two subproblems by setting (x + 5.07142857) equal to 5.15524302 and -5.15524302.Subproblem 1
x + 5.07142857 = 5.15524302 Simplifying x + 5.07142857 = 5.15524302 Reorder the terms: 5.07142857 + x = 5.15524302 Solving 5.07142857 + x = 5.15524302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.07142857' to each side of the equation. 5.07142857 + -5.07142857 + x = 5.15524302 + -5.07142857 Combine like terms: 5.07142857 + -5.07142857 = 0.00000000 0.00000000 + x = 5.15524302 + -5.07142857 x = 5.15524302 + -5.07142857 Combine like terms: 5.15524302 + -5.07142857 = 0.08381445 x = 0.08381445 Simplifying x = 0.08381445Subproblem 2
x + 5.07142857 = -5.15524302 Simplifying x + 5.07142857 = -5.15524302 Reorder the terms: 5.07142857 + x = -5.15524302 Solving 5.07142857 + x = -5.15524302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.07142857' to each side of the equation. 5.07142857 + -5.07142857 + x = -5.15524302 + -5.07142857 Combine like terms: 5.07142857 + -5.07142857 = 0.00000000 0.00000000 + x = -5.15524302 + -5.07142857 x = -5.15524302 + -5.07142857 Combine like terms: -5.15524302 + -5.07142857 = -10.22667159 x = -10.22667159 Simplifying x = -10.22667159Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.08381445, -10.22667159}
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