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Simplifying 0 = 4x2 + 16x + 17 Reorder the terms: 0 = 17 + 16x + 4x2 Solving 0 = 17 + 16x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -17 = -17 -17 + -16x + -4x2 = 17 + 16x + 4x2 + -17 + -16x + -4x2 Reorder the terms: -17 + -16x + -4x2 = 17 + -17 + 16x + -16x + 4x2 + -4x2 Combine like terms: 17 + -17 = 0 -17 + -16x + -4x2 = 0 + 16x + -16x + 4x2 + -4x2 -17 + -16x + -4x2 = 16x + -16x + 4x2 + -4x2 Combine like terms: 16x + -16x = 0 -17 + -16x + -4x2 = 0 + 4x2 + -4x2 -17 + -16x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -17 + -16x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + 16x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + 16x + 4x2)' equal to zero and attempt to solve: Simplifying 17 + 16x + 4x2 = 0 Solving 17 + 16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.25 + 4x + x2 = 0 Move the constant term to the right: Add '-4.25' to each side of the equation. 4.25 + 4x + -4.25 + x2 = 0 + -4.25 Reorder the terms: 4.25 + -4.25 + 4x + x2 = 0 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + 4x + x2 = 0 + -4.25 4x + x2 = 0 + -4.25 Combine like terms: 0 + -4.25 = -4.25 4x + x2 = -4.25 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -4.25 + 4 Reorder the terms: 4 + 4x + x2 = -4.25 + 4 Combine like terms: -4.25 + 4 = -0.25 4 + 4x + x2 = -0.25 Factor a perfect square on the left side: (x + 2)(x + 2) = -0.25 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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