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Simplifying 12x2 + 10x + 8 = 0 Reorder the terms: 8 + 10x + 12x2 = 0 Solving 8 + 10x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 5x + 6x2) = 0 Ignore the factor 2.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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