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Simplifying (3x + 1)(4x + 2) = -10 Reorder the terms: (1 + 3x)(4x + 2) = -10 Reorder the terms: (1 + 3x)(2 + 4x) = -10 Multiply (1 + 3x) * (2 + 4x) (1(2 + 4x) + 3x * (2 + 4x)) = -10 ((2 * 1 + 4x * 1) + 3x * (2 + 4x)) = -10 ((2 + 4x) + 3x * (2 + 4x)) = -10 (2 + 4x + (2 * 3x + 4x * 3x)) = -10 (2 + 4x + (6x + 12x2)) = -10 Combine like terms: 4x + 6x = 10x (2 + 10x + 12x2) = -10 Solving 2 + 10x + 12x2 = -10 Solving for variable 'x'. Reorder the terms: 2 + 10 + 10x + 12x2 = -10 + 10 Combine like terms: 2 + 10 = 12 12 + 10x + 12x2 = -10 + 10 Combine like terms: -10 + 10 = 0 12 + 10x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 5x + 6x2) = 0 Ignore the factor 2.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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