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Simplifying x + 4x(4x + 32) = 12 Reorder the terms: x + 4x(32 + 4x) = 12 x + (32 * 4x + 4x * 4x) = 12 x + (128x + 16x2) = 12 Combine like terms: x + 128x = 129x 129x + 16x2 = 12 Solving 129x + 16x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 129x + 16x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 129x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.75 + 8.0625x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 8.0625x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 8.0625x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 8.0625x + x2 = 0 + 0.75 8.0625x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 8.0625x + x2 = 0.75 The x term is 8.0625x. Take half its coefficient (4.03125). Square it (16.25097656) and add it to both sides. Add '16.25097656' to each side of the equation. 8.0625x + 16.25097656 + x2 = 0.75 + 16.25097656 Reorder the terms: 16.25097656 + 8.0625x + x2 = 0.75 + 16.25097656 Combine like terms: 0.75 + 16.25097656 = 17.00097656 16.25097656 + 8.0625x + x2 = 17.00097656 Factor a perfect square on the left side: (x + 4.03125)(x + 4.03125) = 17.00097656 Calculate the square root of the right side: 4.123224049 Break this problem into two subproblems by setting (x + 4.03125) equal to 4.123224049 and -4.123224049.Subproblem 1
x + 4.03125 = 4.123224049 Simplifying x + 4.03125 = 4.123224049 Reorder the terms: 4.03125 + x = 4.123224049 Solving 4.03125 + x = 4.123224049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.03125' to each side of the equation. 4.03125 + -4.03125 + x = 4.123224049 + -4.03125 Combine like terms: 4.03125 + -4.03125 = 0.00000 0.00000 + x = 4.123224049 + -4.03125 x = 4.123224049 + -4.03125 Combine like terms: 4.123224049 + -4.03125 = 0.091974049 x = 0.091974049 Simplifying x = 0.091974049Subproblem 2
x + 4.03125 = -4.123224049 Simplifying x + 4.03125 = -4.123224049 Reorder the terms: 4.03125 + x = -4.123224049 Solving 4.03125 + x = -4.123224049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.03125' to each side of the equation. 4.03125 + -4.03125 + x = -4.123224049 + -4.03125 Combine like terms: 4.03125 + -4.03125 = 0.00000 0.00000 + x = -4.123224049 + -4.03125 x = -4.123224049 + -4.03125 Combine like terms: -4.123224049 + -4.03125 = -8.154474049 x = -8.154474049 Simplifying x = -8.154474049Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.091974049, -8.154474049}
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