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Simplifying (4x2 + 5)(2) + (2x + -3)(8x) = 0 Reorder the terms: (5 + 4x2)(2) + (2x + -3)(8x) = 0 Reorder the terms for easier multiplication: 2(5 + 4x2) + (2x + -3)(8x) = 0 (5 * 2 + 4x2 * 2) + (2x + -3)(8x) = 0 (10 + 8x2) + (2x + -3)(8x) = 0 Reorder the terms: 10 + 8x2 + (-3 + 2x)(8x) = 0 Remove parenthesis around (8x) 10 + 8x2 + (-3 + 2x) * 8x = 0 Reorder the terms for easier multiplication: 10 + 8x2 + 8x(-3 + 2x) = 0 10 + 8x2 + (-3 * 8x + 2x * 8x) = 0 10 + 8x2 + (-24x + 16x2) = 0 Reorder the terms: 10 + -24x + 8x2 + 16x2 = 0 Combine like terms: 8x2 + 16x2 = 24x2 10 + -24x + 24x2 = 0 Solving 10 + -24x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -12x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -12x + 12x2)' equal to zero and attempt to solve: Simplifying 5 + -12x + 12x2 = 0 Solving 5 + -12x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + -1x + x2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + -1x + -0.4166666667 + x2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + -1x + x2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + -0.4166666667 -1x + x2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 -1x + x2 = -0.4166666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.4166666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.4166666667 + 0.25 Combine like terms: -0.4166666667 + 0.25 = -0.1666666667 0.25 + -1x + x2 = -0.1666666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.1666666667 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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