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Simplifying 0 = 6x2 + 7x + -2x + 3 Reorder the terms: 0 = 3 + 7x + -2x + 6x2 Combine like terms: 7x + -2x = 5x 0 = 3 + 5x + 6x2 Solving 0 = 3 + 5x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -5x + -6x2 = 3 + 5x + 6x2 + -3 + -5x + -6x2 Reorder the terms: -3 + -5x + -6x2 = 3 + -3 + 5x + -5x + 6x2 + -6x2 Combine like terms: 3 + -3 = 0 -3 + -5x + -6x2 = 0 + 5x + -5x + 6x2 + -6x2 -3 + -5x + -6x2 = 5x + -5x + 6x2 + -6x2 Combine like terms: 5x + -5x = 0 -3 + -5x + -6x2 = 0 + 6x2 + -6x2 -3 + -5x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -3 + -5x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 5x + 6x2) = 0 Ignore the factor -1.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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