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Simplifying (4x2 + 2x + 8) + -1(-6x2 + -8x + 4) = 0 Reorder the terms: (8 + 2x + 4x2) + -1(-6x2 + -8x + 4) = 0 Remove parenthesis around (8 + 2x + 4x2) 8 + 2x + 4x2 + -1(-6x2 + -8x + 4) = 0 Reorder the terms: 8 + 2x + 4x2 + -1(4 + -8x + -6x2) = 0 8 + 2x + 4x2 + (4 * -1 + -8x * -1 + -6x2 * -1) = 0 8 + 2x + 4x2 + (-4 + 8x + 6x2) = 0 Reorder the terms: 8 + -4 + 2x + 8x + 4x2 + 6x2 = 0 Combine like terms: 8 + -4 = 4 4 + 2x + 8x + 4x2 + 6x2 = 0 Combine like terms: 2x + 8x = 10x 4 + 10x + 4x2 + 6x2 = 0 Combine like terms: 4x2 + 6x2 = 10x2 4 + 10x + 10x2 = 0 Solving 4 + 10x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 5x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 5x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + 5x + 5x2 = 0 Solving 2 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x + x2 = 0 + -0.4 x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 x + x2 = -0.4 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. + 0.25 + x2 = -0.4 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.4 + 0.25 Combine like terms: -0.4 + 0.25 = -0.15 1.25 + x2 = -0.15 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.15 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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