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Simplifying 5(4x2 + -12x + 9) + 4 = -56 Reorder the terms: 5(9 + -12x + 4x2) + 4 = -56 (9 * 5 + -12x * 5 + 4x2 * 5) + 4 = -56 (45 + -60x + 20x2) + 4 = -56 Reorder the terms: 45 + 4 + -60x + 20x2 = -56 Combine like terms: 45 + 4 = 49 49 + -60x + 20x2 = -56 Solving 49 + -60x + 20x2 = -56 Solving for variable 'x'. Reorder the terms: 49 + 56 + -60x + 20x2 = -56 + 56 Combine like terms: 49 + 56 = 105 105 + -60x + 20x2 = -56 + 56 Combine like terms: -56 + 56 = 0 105 + -60x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(21 + -12x + 4x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(21 + -12x + 4x2)' equal to zero and attempt to solve: Simplifying 21 + -12x + 4x2 = 0 Solving 21 + -12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.25 + -3x + x2 = 0 Move the constant term to the right: Add '-5.25' to each side of the equation. 5.25 + -3x + -5.25 + x2 = 0 + -5.25 Reorder the terms: 5.25 + -5.25 + -3x + x2 = 0 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + -3x + x2 = 0 + -5.25 -3x + x2 = 0 + -5.25 Combine like terms: 0 + -5.25 = -5.25 -3x + x2 = -5.25 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -5.25 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -5.25 + 2.25 Combine like terms: -5.25 + 2.25 = -3 2.25 + -3x + x2 = -3 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -3 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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