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Simplifying 8x2 = 26x + -84 Reorder the terms: 8x2 = -84 + 26x Solving 8x2 = -84 + 26x Solving for variable 'x'. Reorder the terms: 84 + -26x + 8x2 = -84 + 26x + 84 + -26x Reorder the terms: 84 + -26x + 8x2 = -84 + 84 + 26x + -26x Combine like terms: -84 + 84 = 0 84 + -26x + 8x2 = 0 + 26x + -26x 84 + -26x + 8x2 = 26x + -26x Combine like terms: 26x + -26x = 0 84 + -26x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(42 + -13x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(42 + -13x + 4x2)' equal to zero and attempt to solve: Simplifying 42 + -13x + 4x2 = 0 Solving 42 + -13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 10.5 + -3.25x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -3.25x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -3.25x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -3.25x + x2 = 0 + -10.5 -3.25x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -3.25x + x2 = -10.5 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = -10.5 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = -10.5 + 2.640625 Combine like terms: -10.5 + 2.640625 = -7.859375 2.640625 + -3.25x + x2 = -7.859375 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = -7.859375 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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