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Simplifying (3x2 + -7x + -4) + -1(6x2 + -6x + 1) = 0 Reorder the terms: (-4 + -7x + 3x2) + -1(6x2 + -6x + 1) = 0 Remove parenthesis around (-4 + -7x + 3x2) -4 + -7x + 3x2 + -1(6x2 + -6x + 1) = 0 Reorder the terms: -4 + -7x + 3x2 + -1(1 + -6x + 6x2) = 0 -4 + -7x + 3x2 + (1 * -1 + -6x * -1 + 6x2 * -1) = 0 -4 + -7x + 3x2 + (-1 + 6x + -6x2) = 0 Reorder the terms: -4 + -1 + -7x + 6x + 3x2 + -6x2 = 0 Combine like terms: -4 + -1 = -5 -5 + -7x + 6x + 3x2 + -6x2 = 0 Combine like terms: -7x + 6x = -1x -5 + -1x + 3x2 + -6x2 = 0 Combine like terms: 3x2 + -6x2 = -3x2 -5 + -1x + -3x2 = 0 Solving -5 + -1x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + x + 3x2)' equal to zero and attempt to solve: Simplifying 5 + x + 3x2 = 0 Solving 5 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 0.3333333333x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 0.3333333333x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 0.3333333333x + x2 = 0 + -1.666666667 0.3333333333x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 0.3333333333x + x2 = -1.666666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = -1.666666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = -1.666666667 + 0.25 Combine like terms: -1.666666667 + 0.25 = -1.416666667 0.25 + 0.3333333333x + x2 = -1.416666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.416666667 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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