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Simplifying 3x + -1(7x2 + 8x + 7) + 3(-1x2 + -6) = 0 Reorder the terms: 3x + -1(7 + 8x + 7x2) + 3(-1x2 + -6) = 0 3x + (7 * -1 + 8x * -1 + 7x2 * -1) + 3(-1x2 + -6) = 0 3x + (-7 + -8x + -7x2) + 3(-1x2 + -6) = 0 Reorder the terms: 3x + -7 + -8x + -7x2 + 3(-6 + -1x2) = 0 3x + -7 + -8x + -7x2 + (-6 * 3 + -1x2 * 3) = 0 3x + -7 + -8x + -7x2 + (-18 + -3x2) = 0 Reorder the terms: -7 + -18 + 3x + -8x + -7x2 + -3x2 = 0 Combine like terms: -7 + -18 = -25 -25 + 3x + -8x + -7x2 + -3x2 = 0 Combine like terms: 3x + -8x = -5x -25 + -5x + -7x2 + -3x2 = 0 Combine like terms: -7x2 + -3x2 = -10x2 -25 + -5x + -10x2 = 0 Solving -25 + -5x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-5'. -5(5 + x + 2x2) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(5 + x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + x + 2x2 = 0 Solving 5 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 0.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 0.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 0.5x + x2 = 0 + -2.5 0.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 0.5x + x2 = -2.5 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 = -2.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -2.5 + 0.25 Combine like terms: -2.5 + 0.25 = -2.25 0.25 + 0.5x + x2 = -2.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -2.25 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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