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Simplifying 18x2 = 15x + -12 Reorder the terms: 18x2 = -12 + 15x Solving 18x2 = -12 + 15x Solving for variable 'x'. Reorder the terms: 12 + -15x + 18x2 = -12 + 15x + 12 + -15x Reorder the terms: 12 + -15x + 18x2 = -12 + 12 + 15x + -15x Combine like terms: -12 + 12 = 0 12 + -15x + 18x2 = 0 + 15x + -15x 12 + -15x + 18x2 = 15x + -15x Combine like terms: 15x + -15x = 0 12 + -15x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -5x + 6x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + -5x + 6x2)' equal to zero and attempt to solve: Simplifying 4 + -5x + 6x2 = 0 Solving 4 + -5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -0.8333333333x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -0.8333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -0.8333333333x + x2 = 0 + -0.6666666667 -0.8333333333x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -0.8333333333x + x2 = -0.6666666667 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = -0.6666666667 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = -0.6666666667 + 0.1736111111 Combine like terms: -0.6666666667 + 0.1736111111 = -0.4930555556 0.1736111111 + -0.8333333333x + x2 = -0.4930555556 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = -0.4930555556 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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