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Simplifying 48x * 48x + 24x = -3 Reorder the terms for easier multiplication: 48 * 48x * x + 24x = -3 Multiply 48 * 48 2304x * x + 24x = -3 Multiply x * x 2304x2 + 24x = -3 Reorder the terms: 24x + 2304x2 = -3 Solving 24x + 2304x2 = -3 Solving for variable 'x'. Reorder the terms: 3 + 24x + 2304x2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + 24x + 2304x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 8x + 768x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 8x + 768x2)' equal to zero and attempt to solve: Simplifying 1 + 8x + 768x2 = 0 Solving 1 + 8x + 768x2 = 0 Begin completing the square. Divide all terms by 768 the coefficient of the squared term: Divide each side by '768'. 0.001302083333 + 0.01041666667x + x2 = 0 Move the constant term to the right: Add '-0.001302083333' to each side of the equation. 0.001302083333 + 0.01041666667x + -0.001302083333 + x2 = 0 + -0.001302083333 Reorder the terms: 0.001302083333 + -0.001302083333 + 0.01041666667x + x2 = 0 + -0.001302083333 Combine like terms: 0.001302083333 + -0.001302083333 = 0.000000000000 0.000000000000 + 0.01041666667x + x2 = 0 + -0.001302083333 0.01041666667x + x2 = 0 + -0.001302083333 Combine like terms: 0 + -0.001302083333 = -0.001302083333 0.01041666667x + x2 = -0.001302083333 The x term is 0.01041666667x. Take half its coefficient (0.005208333335). Square it (0.00002712673613) and add it to both sides. Add '0.00002712673613' to each side of the equation. 0.01041666667x + 0.00002712673613 + x2 = -0.001302083333 + 0.00002712673613 Reorder the terms: 0.00002712673613 + 0.01041666667x + x2 = -0.001302083333 + 0.00002712673613 Combine like terms: -0.001302083333 + 0.00002712673613 = -0.00127495659687 0.00002712673613 + 0.01041666667x + x2 = -0.00127495659687 Factor a perfect square on the left side: (x + 0.005208333335)(x + 0.005208333335) = -0.00127495659687 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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