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Simplifying -6x + -1 + -24x2 = 0 Reorder the terms: -1 + -6x + -24x2 = 0 Solving -1 + -6x + -24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 6x + 24x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 6x + 24x2)' equal to zero and attempt to solve: Simplifying 1 + 6x + 24x2 = 0 Solving 1 + 6x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.04166666667 + 0.25x + x2 = 0 Move the constant term to the right: Add '-0.04166666667' to each side of the equation. 0.04166666667 + 0.25x + -0.04166666667 + x2 = 0 + -0.04166666667 Reorder the terms: 0.04166666667 + -0.04166666667 + 0.25x + x2 = 0 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + 0.25x + x2 = 0 + -0.04166666667 0.25x + x2 = 0 + -0.04166666667 Combine like terms: 0 + -0.04166666667 = -0.04166666667 0.25x + x2 = -0.04166666667 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = -0.04166666667 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = -0.04166666667 + 0.015625 Combine like terms: -0.04166666667 + 0.015625 = -0.02604166667 0.015625 + 0.25x + x2 = -0.02604166667 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = -0.02604166667 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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