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Simplifying -6x2 + -5x + -11 = 0 Reorder the terms: -11 + -5x + -6x2 = 0 Solving -11 + -5x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 5x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 5x + 6x2)' equal to zero and attempt to solve: Simplifying 11 + 5x + 6x2 = 0 Solving 11 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.833333333 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '-1.833333333' to each side of the equation. 1.833333333 + 0.8333333333x + -1.833333333 + x2 = 0 + -1.833333333 Reorder the terms: 1.833333333 + -1.833333333 + 0.8333333333x + x2 = 0 + -1.833333333 Combine like terms: 1.833333333 + -1.833333333 = 0.000000000 0.000000000 + 0.8333333333x + x2 = 0 + -1.833333333 0.8333333333x + x2 = 0 + -1.833333333 Combine like terms: 0 + -1.833333333 = -1.833333333 0.8333333333x + x2 = -1.833333333 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 = -1.833333333 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = -1.833333333 + 0.1736111111 Combine like terms: -1.833333333 + 0.1736111111 = -1.6597222219 0.1736111111 + 0.8333333333x + x2 = -1.6597222219 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = -1.6597222219 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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