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Simplifying 0 = 2x2 + 7x + 8 Reorder the terms: 0 = 8 + 7x + 2x2 Solving 0 = 8 + 7x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + -7x + -2x2 = 8 + 7x + 2x2 + -8 + -7x + -2x2 Reorder the terms: -8 + -7x + -2x2 = 8 + -8 + 7x + -7x + 2x2 + -2x2 Combine like terms: 8 + -8 = 0 -8 + -7x + -2x2 = 0 + 7x + -7x + 2x2 + -2x2 -8 + -7x + -2x2 = 7x + -7x + 2x2 + -2x2 Combine like terms: 7x + -7x = 0 -8 + -7x + -2x2 = 0 + 2x2 + -2x2 -8 + -7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -8 + -7x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 7x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying 8 + 7x + 2x2 = 0 Solving 8 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + 3.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 3.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 3.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3.5x + x2 = 0 + -4 3.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 3.5x + x2 = -4 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -4 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -4 + 3.0625 Combine like terms: -4 + 3.0625 = -0.9375 3.0625 + 3.5x + x2 = -0.9375 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = -0.9375 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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