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Simplifying 3x + -1 + 8x2(4) = 0 Reorder the terms for easier multiplication: 3x + -1 + 8 * 4x2 = 0 Multiply 8 * 4 3x + -1 + 32x2 = 0 Reorder the terms: -1 + 3x + 32x2 = 0 Solving -1 + 3x + 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'. -0.03125 + 0.09375x + x2 = 0 Move the constant term to the right: Add '0.03125' to each side of the equation. -0.03125 + 0.09375x + 0.03125 + x2 = 0 + 0.03125 Reorder the terms: -0.03125 + 0.03125 + 0.09375x + x2 = 0 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + 0.09375x + x2 = 0 + 0.03125 0.09375x + x2 = 0 + 0.03125 Combine like terms: 0 + 0.03125 = 0.03125 0.09375x + x2 = 0.03125 The x term is 0.09375x. Take half its coefficient (0.046875). Square it (0.002197265625) and add it to both sides. Add '0.002197265625' to each side of the equation. 0.09375x + 0.002197265625 + x2 = 0.03125 + 0.002197265625 Reorder the terms: 0.002197265625 + 0.09375x + x2 = 0.03125 + 0.002197265625 Combine like terms: 0.03125 + 0.002197265625 = 0.033447265625 0.002197265625 + 0.09375x + x2 = 0.033447265625 Factor a perfect square on the left side: (x + 0.046875)(x + 0.046875) = 0.033447265625 Calculate the square root of the right side: 0.182885936 Break this problem into two subproblems by setting (x + 0.046875) equal to 0.182885936 and -0.182885936.Subproblem 1
x + 0.046875 = 0.182885936 Simplifying x + 0.046875 = 0.182885936 Reorder the terms: 0.046875 + x = 0.182885936 Solving 0.046875 + x = 0.182885936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.046875' to each side of the equation. 0.046875 + -0.046875 + x = 0.182885936 + -0.046875 Combine like terms: 0.046875 + -0.046875 = 0.000000 0.000000 + x = 0.182885936 + -0.046875 x = 0.182885936 + -0.046875 Combine like terms: 0.182885936 + -0.046875 = 0.136010936 x = 0.136010936 Simplifying x = 0.136010936Subproblem 2
x + 0.046875 = -0.182885936 Simplifying x + 0.046875 = -0.182885936 Reorder the terms: 0.046875 + x = -0.182885936 Solving 0.046875 + x = -0.182885936 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.046875' to each side of the equation. 0.046875 + -0.046875 + x = -0.182885936 + -0.046875 Combine like terms: 0.046875 + -0.046875 = 0.000000 0.000000 + x = -0.182885936 + -0.046875 x = -0.182885936 + -0.046875 Combine like terms: -0.182885936 + -0.046875 = -0.229760936 x = -0.229760936 Simplifying x = -0.229760936Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.136010936, -0.229760936}
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