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Simplifying 34x2 + 16x + 22 = 0 Reorder the terms: 22 + 16x + 34x2 = 0 Solving 22 + 16x + 34x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + 8x + 17x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + 8x + 17x2)' equal to zero and attempt to solve: Simplifying 11 + 8x + 17x2 = 0 Solving 11 + 8x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 0.6470588235 + 0.4705882353x + x2 = 0 Move the constant term to the right: Add '-0.6470588235' to each side of the equation. 0.6470588235 + 0.4705882353x + -0.6470588235 + x2 = 0 + -0.6470588235 Reorder the terms: 0.6470588235 + -0.6470588235 + 0.4705882353x + x2 = 0 + -0.6470588235 Combine like terms: 0.6470588235 + -0.6470588235 = 0.0000000000 0.0000000000 + 0.4705882353x + x2 = 0 + -0.6470588235 0.4705882353x + x2 = 0 + -0.6470588235 Combine like terms: 0 + -0.6470588235 = -0.6470588235 0.4705882353x + x2 = -0.6470588235 The x term is 0.4705882353x. Take half its coefficient (0.2352941177). Square it (0.05536332182) and add it to both sides. Add '0.05536332182' to each side of the equation. 0.4705882353x + 0.05536332182 + x2 = -0.6470588235 + 0.05536332182 Reorder the terms: 0.05536332182 + 0.4705882353x + x2 = -0.6470588235 + 0.05536332182 Combine like terms: -0.6470588235 + 0.05536332182 = -0.59169550168 0.05536332182 + 0.4705882353x + x2 = -0.59169550168 Factor a perfect square on the left side: (x + 0.2352941177)(x + 0.2352941177) = -0.59169550168 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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