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Simplifying 8x2 + 16x + 42 = 0 Reorder the terms: 42 + 16x + 8x2 = 0 Solving 42 + 16x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 8x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + 8x + 4x2)' equal to zero and attempt to solve: Simplifying 21 + 8x + 4x2 = 0 Solving 21 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.25 + 2x + x2 = 0 Move the constant term to the right: Add '-5.25' to each side of the equation. 5.25 + 2x + -5.25 + x2 = 0 + -5.25 Reorder the terms: 5.25 + -5.25 + 2x + x2 = 0 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + 2x + x2 = 0 + -5.25 2x + x2 = 0 + -5.25 Combine like terms: 0 + -5.25 = -5.25 2x + x2 = -5.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -5.25 + 1 Reorder the terms: 1 + 2x + x2 = -5.25 + 1 Combine like terms: -5.25 + 1 = -4.25 1 + 2x + x2 = -4.25 Factor a perfect square on the left side: (x + 1)(x + 1) = -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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