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Simplifying -6x2 = 5x + 6 Reorder the terms: -6x2 = 6 + 5x Solving -6x2 = 6 + 5x Solving for variable 'x'. Reorder the terms: -6 + -5x + -6x2 = 6 + 5x + -6 + -5x Reorder the terms: -6 + -5x + -6x2 = 6 + -6 + 5x + -5x Combine like terms: 6 + -6 = 0 -6 + -5x + -6x2 = 0 + 5x + -5x -6 + -5x + -6x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -6 + -5x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 5x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 5x + 6x2)' equal to zero and attempt to solve: Simplifying 6 + 5x + 6x2 = 0 Solving 6 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.8333333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 0.8333333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.8333333333x + x2 = 0 + -1 0.8333333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.8333333333x + x2 = -1 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 = -1 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = -1 + 0.1736111111 Combine like terms: -1 + 0.1736111111 = -0.8263888889 0.1736111111 + 0.8333333333x + x2 = -0.8263888889 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = -0.8263888889 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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