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Simplifying 8x2 + 40x + 84 = 0 Reorder the terms: 84 + 40x + 8x2 = 0 Solving 84 + 40x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(21 + 10x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(21 + 10x + 2x2)' equal to zero and attempt to solve: Simplifying 21 + 10x + 2x2 = 0 Solving 21 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + 5x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + 5x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + 5x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + 5x + x2 = 0 + -10.5 5x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 5x + x2 = -10.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -10.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -10.5 + 6.25 Combine like terms: -10.5 + 6.25 = -4.25 6.25 + 5x + x2 = -4.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -4.25 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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