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Simplifying 8x(1 + -4x) + 7(5 + -1x) = 0 (1 * 8x + -4x * 8x) + 7(5 + -1x) = 0 (8x + -32x2) + 7(5 + -1x) = 0 8x + -32x2 + (5 * 7 + -1x * 7) = 0 8x + -32x2 + (35 + -7x) = 0 Reorder the terms: 35 + 8x + -7x + -32x2 = 0 Combine like terms: 8x + -7x = 1x 35 + 1x + -32x2 = 0 Solving 35 + 1x + -32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -32 the coefficient of the squared term: Divide each side by '-32'. -1.09375 + -0.03125x + x2 = 0 Move the constant term to the right: Add '1.09375' to each side of the equation. -1.09375 + -0.03125x + 1.09375 + x2 = 0 + 1.09375 Reorder the terms: -1.09375 + 1.09375 + -0.03125x + x2 = 0 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + -0.03125x + x2 = 0 + 1.09375 -0.03125x + x2 = 0 + 1.09375 Combine like terms: 0 + 1.09375 = 1.09375 -0.03125x + x2 = 1.09375 The x term is -0.03125x. Take half its coefficient (-0.015625). Square it (0.000244140625) and add it to both sides. Add '0.000244140625' to each side of the equation. -0.03125x + 0.000244140625 + x2 = 1.09375 + 0.000244140625 Reorder the terms: 0.000244140625 + -0.03125x + x2 = 1.09375 + 0.000244140625 Combine like terms: 1.09375 + 0.000244140625 = 1.093994140625 0.000244140625 + -0.03125x + x2 = 1.093994140625 Factor a perfect square on the left side: (x + -0.015625)(x + -0.015625) = 1.093994140625 Calculate the square root of the right side: 1.045941748 Break this problem into two subproblems by setting (x + -0.015625) equal to 1.045941748 and -1.045941748.Subproblem 1
x + -0.015625 = 1.045941748 Simplifying x + -0.015625 = 1.045941748 Reorder the terms: -0.015625 + x = 1.045941748 Solving -0.015625 + x = 1.045941748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.015625' to each side of the equation. -0.015625 + 0.015625 + x = 1.045941748 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + x = 1.045941748 + 0.015625 x = 1.045941748 + 0.015625 Combine like terms: 1.045941748 + 0.015625 = 1.061566748 x = 1.061566748 Simplifying x = 1.061566748Subproblem 2
x + -0.015625 = -1.045941748 Simplifying x + -0.015625 = -1.045941748 Reorder the terms: -0.015625 + x = -1.045941748 Solving -0.015625 + x = -1.045941748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.015625' to each side of the equation. -0.015625 + 0.015625 + x = -1.045941748 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + x = -1.045941748 + 0.015625 x = -1.045941748 + 0.015625 Combine like terms: -1.045941748 + 0.015625 = -1.030316748 x = -1.030316748 Simplifying x = -1.030316748Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.061566748, -1.030316748}
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