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Simplifying 3x(x + 16) = 32 Reorder the terms: 3x(16 + x) = 32 (16 * 3x + x * 3x) = 32 (48x + 3x2) = 32 Solving 48x + 3x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 48x + 3x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 48x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.66666667 + 16x + x2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + 16x + 10.66666667 + x2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + 16x + x2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + 16x + x2 = 0 + 10.66666667 16x + x2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 16x + x2 = 10.66666667 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 = 10.66666667 + 64 Reorder the terms: 64 + 16x + x2 = 10.66666667 + 64 Combine like terms: 10.66666667 + 64 = 74.66666667 64 + 16x + x2 = 74.66666667 Factor a perfect square on the left side: (x + 8)(x + 8) = 74.66666667 Calculate the square root of the right side: 8.640987598 Break this problem into two subproblems by setting (x + 8) equal to 8.640987598 and -8.640987598.Subproblem 1
x + 8 = 8.640987598 Simplifying x + 8 = 8.640987598 Reorder the terms: 8 + x = 8.640987598 Solving 8 + x = 8.640987598 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 = 8.640987598 + -8 Combine like terms: 8 + -8 = 0 0 + x = 8.640987598 + -8 x = 8.640987598 + -8 Combine like terms: 8.640987598 + -8 = 0.640987598 x = 0.640987598 Simplifying x = 0.640987598Subproblem 2
x + 8 = -8.640987598 Simplifying x + 8 = -8.640987598 Reorder the terms: 8 + x = -8.640987598 Solving 8 + x = -8.640987598 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 = -8.640987598 + -8 Combine like terms: 8 + -8 = 0 0 + x = -8.640987598 + -8 x = -8.640987598 + -8 Combine like terms: -8.640987598 + -8 = -16.640987598 x = -16.640987598 Simplifying x = -16.640987598Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.640987598, -16.640987598}
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