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Simplifying 106x2 + -40x + 100 = 0 Reorder the terms: 100 + -40x + 106x2 = 0 Solving 100 + -40x + 106x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(50 + -20x + 53x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + -20x + 53x2)' equal to zero and attempt to solve: Simplifying 50 + -20x + 53x2 = 0 Solving 50 + -20x + 53x2 = 0 Begin completing the square. Divide all terms by 53 the coefficient of the squared term: Divide each side by '53'. 0.9433962264 + -0.3773584906x + x2 = 0 Move the constant term to the right: Add '-0.9433962264' to each side of the equation. 0.9433962264 + -0.3773584906x + -0.9433962264 + x2 = 0 + -0.9433962264 Reorder the terms: 0.9433962264 + -0.9433962264 + -0.3773584906x + x2 = 0 + -0.9433962264 Combine like terms: 0.9433962264 + -0.9433962264 = 0.0000000000 0.0000000000 + -0.3773584906x + x2 = 0 + -0.9433962264 -0.3773584906x + x2 = 0 + -0.9433962264 Combine like terms: 0 + -0.9433962264 = -0.9433962264 -0.3773584906x + x2 = -0.9433962264 The x term is -0.3773584906x. Take half its coefficient (-0.1886792453). Square it (0.03559985761) and add it to both sides. Add '0.03559985761' to each side of the equation. -0.3773584906x + 0.03559985761 + x2 = -0.9433962264 + 0.03559985761 Reorder the terms: 0.03559985761 + -0.3773584906x + x2 = -0.9433962264 + 0.03559985761 Combine like terms: -0.9433962264 + 0.03559985761 = -0.90779636879 0.03559985761 + -0.3773584906x + x2 = -0.90779636879 Factor a perfect square on the left side: (x + -0.1886792453)(x + -0.1886792453) = -0.90779636879 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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