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Simplifying 22x2 + -20x = -180 Reorder the terms: -20x + 22x2 = -180 Solving -20x + 22x2 = -180 Solving for variable 'x'. Reorder the terms: 180 + -20x + 22x2 = -180 + 180 Combine like terms: -180 + 180 = 0 180 + -20x + 22x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(90 + -10x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(90 + -10x + 11x2)' equal to zero and attempt to solve: Simplifying 90 + -10x + 11x2 = 0 Solving 90 + -10x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 8.181818182 + -0.9090909091x + x2 = 0 Move the constant term to the right: Add '-8.181818182' to each side of the equation. 8.181818182 + -0.9090909091x + -8.181818182 + x2 = 0 + -8.181818182 Reorder the terms: 8.181818182 + -8.181818182 + -0.9090909091x + x2 = 0 + -8.181818182 Combine like terms: 8.181818182 + -8.181818182 = 0.000000000 0.000000000 + -0.9090909091x + x2 = 0 + -8.181818182 -0.9090909091x + x2 = 0 + -8.181818182 Combine like terms: 0 + -8.181818182 = -8.181818182 -0.9090909091x + x2 = -8.181818182 The x term is -0.9090909091x. Take half its coefficient (-0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. -0.9090909091x + 0.2066115703 + x2 = -8.181818182 + 0.2066115703 Reorder the terms: 0.2066115703 + -0.9090909091x + x2 = -8.181818182 + 0.2066115703 Combine like terms: -8.181818182 + 0.2066115703 = -7.9752066117 0.2066115703 + -0.9090909091x + x2 = -7.9752066117 Factor a perfect square on the left side: (x + -0.4545454546)(x + -0.4545454546) = -7.9752066117 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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