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Simplifying -6x2 + 5x + -1(6x2 + -5x + 6) = 0 Reorder the terms: -6x2 + 5x + -1(6 + -5x + 6x2) = 0 -6x2 + 5x + (6 * -1 + -5x * -1 + 6x2 * -1) = 0 -6x2 + 5x + (-6 + 5x + -6x2) = 0 Reorder the terms: -6 + 5x + 5x + -6x2 + -6x2 = 0 Combine like terms: 5x + 5x = 10x -6 + 10x + -6x2 + -6x2 = 0 Combine like terms: -6x2 + -6x2 = -12x2 -6 + 10x + -12x2 = 0 Solving -6 + 10x + -12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 5x + -6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 5x + -6x2)' equal to zero and attempt to solve: Simplifying -3 + 5x + -6x2 = 0 Solving -3 + 5x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.5 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -0.8333333333x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -0.8333333333x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -0.8333333333x + x2 = 0 + -0.5 -0.8333333333x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -0.8333333333x + x2 = -0.5 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 = -0.5 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = -0.5 + 0.1736111111 Combine like terms: -0.5 + 0.1736111111 = -0.3263888889 0.1736111111 + -0.8333333333x + x2 = -0.3263888889 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = -0.3263888889 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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