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Simplifying 6(x + -8) + -1x(x + 4) + 9(x2 + 6) = 0 Reorder the terms: 6(-8 + x) + -1x(x + 4) + 9(x2 + 6) = 0 (-8 * 6 + x * 6) + -1x(x + 4) + 9(x2 + 6) = 0 (-48 + 6x) + -1x(x + 4) + 9(x2 + 6) = 0 Reorder the terms: -48 + 6x + -1x(4 + x) + 9(x2 + 6) = 0 -48 + 6x + (4 * -1x + x * -1x) + 9(x2 + 6) = 0 -48 + 6x + (-4x + -1x2) + 9(x2 + 6) = 0 Reorder the terms: -48 + 6x + -4x + -1x2 + 9(6 + x2) = 0 -48 + 6x + -4x + -1x2 + (6 * 9 + x2 * 9) = 0 -48 + 6x + -4x + -1x2 + (54 + 9x2) = 0 Reorder the terms: -48 + 54 + 6x + -4x + -1x2 + 9x2 = 0 Combine like terms: -48 + 54 = 6 6 + 6x + -4x + -1x2 + 9x2 = 0 Combine like terms: 6x + -4x = 2x 6 + 2x + -1x2 + 9x2 = 0 Combine like terms: -1x2 + 9x2 = 8x2 6 + 2x + 8x2 = 0 Solving 6 + 2x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + x + 4x2)' equal to zero and attempt to solve: Simplifying 3 + x + 4x2 = 0 Solving 3 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 0.25x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.25x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.25x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.25x + x2 = 0 + -0.75 0.25x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 0.25x + x2 = -0.75 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. 0.25x + 0.25 + x2 = -0.75 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = -0.75 + 0.25 Combine like terms: -0.75 + 0.25 = -0.5 0.25 + 0.25x + x2 = -0.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.5 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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