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Simplifying 48x2 + 30x + 10 = 0 Reorder the terms: 10 + 30x + 48x2 = 0 Solving 10 + 30x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 15x + 24x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 15x + 24x2)' equal to zero and attempt to solve: Simplifying 5 + 15x + 24x2 = 0 Solving 5 + 15x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.2083333333 + 0.625x + x2 = 0 Move the constant term to the right: Add '-0.2083333333' to each side of the equation. 0.2083333333 + 0.625x + -0.2083333333 + x2 = 0 + -0.2083333333 Reorder the terms: 0.2083333333 + -0.2083333333 + 0.625x + x2 = 0 + -0.2083333333 Combine like terms: 0.2083333333 + -0.2083333333 = 0.0000000000 0.0000000000 + 0.625x + x2 = 0 + -0.2083333333 0.625x + x2 = 0 + -0.2083333333 Combine like terms: 0 + -0.2083333333 = -0.2083333333 0.625x + x2 = -0.2083333333 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = -0.2083333333 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = -0.2083333333 + 0.09765625 Combine like terms: -0.2083333333 + 0.09765625 = -0.1106770833 0.09765625 + 0.625x + x2 = -0.1106770833 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = -0.1106770833 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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