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Simplifying 9x2 + -48x + 64(3x + -8) = 0 Reorder the terms: 9x2 + -48x + 64(-8 + 3x) = 0 9x2 + -48x + (-8 * 64 + 3x * 64) = 0 9x2 + -48x + (-512 + 192x) = 0 Reorder the terms: -512 + -48x + 192x + 9x2 = 0 Combine like terms: -48x + 192x = 144x -512 + 144x + 9x2 = 0 Solving -512 + 144x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -56.88888889 + 16x + x2 = 0 Move the constant term to the right: Add '56.88888889' to each side of the equation. -56.88888889 + 16x + 56.88888889 + x2 = 0 + 56.88888889 Reorder the terms: -56.88888889 + 56.88888889 + 16x + x2 = 0 + 56.88888889 Combine like terms: -56.88888889 + 56.88888889 = 0.00000000 0.00000000 + 16x + x2 = 0 + 56.88888889 16x + x2 = 0 + 56.88888889 Combine like terms: 0 + 56.88888889 = 56.88888889 16x + x2 = 56.88888889 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 56.88888889 + 64 Reorder the terms: 64 + 16x + x2 = 56.88888889 + 64 Combine like terms: 56.88888889 + 64 = 120.88888889 64 + 16x + x2 = 120.88888889 Factor a perfect square on the left side: (x + 8)(x + 8) = 120.88888889 Calculate the square root of the right side: 10.994948335 Break this problem into two subproblems by setting (x + 8) equal to 10.994948335 and -10.994948335.Subproblem 1
x + 8 = 10.994948335 Simplifying x + 8 = 10.994948335 Reorder the terms: 8 + x = 10.994948335 Solving 8 + x = 10.994948335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 10.994948335 + -8 Combine like terms: 8 + -8 = 0 0 + x = 10.994948335 + -8 x = 10.994948335 + -8 Combine like terms: 10.994948335 + -8 = 2.994948335 x = 2.994948335 Simplifying x = 2.994948335Subproblem 2
x + 8 = -10.994948335 Simplifying x + 8 = -10.994948335 Reorder the terms: 8 + x = -10.994948335 Solving 8 + x = -10.994948335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -10.994948335 + -8 Combine like terms: 8 + -8 = 0 0 + x = -10.994948335 + -8 x = -10.994948335 + -8 Combine like terms: -10.994948335 + -8 = -18.994948335 x = -18.994948335 Simplifying x = -18.994948335Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.994948335, -18.994948335}
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