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Simplifying 30x2 + -54x = -72 Reorder the terms: -54x + 30x2 = -72 Solving -54x + 30x2 = -72 Solving for variable 'x'. Reorder the terms: 72 + -54x + 30x2 = -72 + 72 Combine like terms: -72 + 72 = 0 72 + -54x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(12 + -9x + 5x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(12 + -9x + 5x2)' equal to zero and attempt to solve: Simplifying 12 + -9x + 5x2 = 0 Solving 12 + -9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + -1.8x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -1.8x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -1.8x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -1.8x + x2 = 0 + -2.4 -1.8x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -1.8x + x2 = -2.4 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = -2.4 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = -2.4 + 0.81 Combine like terms: -2.4 + 0.81 = -1.59 0.81 + -1.8x + x2 = -1.59 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = -1.59 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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