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Simplifying (3x2 + 5) + (x2 + -4x) + (6x + 7) = 0 Reorder the terms: (5 + 3x2) + (x2 + -4x) + (6x + 7) = 0 Remove parenthesis around (5 + 3x2) 5 + 3x2 + (x2 + -4x) + (6x + 7) = 0 Reorder the terms: 5 + 3x2 + (-4x + x2) + (6x + 7) = 0 Remove parenthesis around (-4x + x2) 5 + 3x2 + -4x + x2 + (6x + 7) = 0 Reorder the terms: 5 + 3x2 + -4x + x2 + (7 + 6x) = 0 Remove parenthesis around (7 + 6x) 5 + 3x2 + -4x + x2 + 7 + 6x = 0 Reorder the terms: 5 + 7 + -4x + 6x + 3x2 + x2 = 0 Combine like terms: 5 + 7 = 12 12 + -4x + 6x + 3x2 + x2 = 0 Combine like terms: -4x + 6x = 2x 12 + 2x + 3x2 + x2 = 0 Combine like terms: 3x2 + x2 = 4x2 12 + 2x + 4x2 = 0 Solving 12 + 2x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + x + 2x2)' equal to zero and attempt to solve: Simplifying 6 + x + 2x2 = 0 Solving 6 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 0.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 0.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 0.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 0.5x + x2 = 0 + -3 0.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 0.5x + x2 = -3 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. 0.5x + 0.25 + x2 = -3 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -3 + 0.25 Combine like terms: -3 + 0.25 = -2.75 0.25 + 0.5x + x2 = -2.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -2.75 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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