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Simplifying -8(x2 + x) = 3 Reorder the terms: -8(x + x2) = 3 (x * -8 + x2 * -8) = 3 (-8x + -8x2) = 3 Solving -8x + -8x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -8x + -8x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -8x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 8x + 8x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 8x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + 8x + 8x2 = 0 Solving 3 + 8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x + x2 = 0 + -0.375 x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 x + x2 = -0.375 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 = -0.375 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.375 + 0.25 Combine like terms: -0.375 + 0.25 = -0.125 1.25 + x2 = -0.125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.125 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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