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Simplifying 0 = 17x2 + 55x + 180 Reorder the terms: 0 = 180 + 55x + 17x2 Solving 0 = 180 + 55x + 17x2 Solving for variable 'x'. Combine like terms: 0 + -180 = -180 -180 + -55x + -17x2 = 180 + 55x + 17x2 + -180 + -55x + -17x2 Reorder the terms: -180 + -55x + -17x2 = 180 + -180 + 55x + -55x + 17x2 + -17x2 Combine like terms: 180 + -180 = 0 -180 + -55x + -17x2 = 0 + 55x + -55x + 17x2 + -17x2 -180 + -55x + -17x2 = 55x + -55x + 17x2 + -17x2 Combine like terms: 55x + -55x = 0 -180 + -55x + -17x2 = 0 + 17x2 + -17x2 -180 + -55x + -17x2 = 17x2 + -17x2 Combine like terms: 17x2 + -17x2 = 0 -180 + -55x + -17x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(180 + 55x + 17x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(180 + 55x + 17x2)' equal to zero and attempt to solve: Simplifying 180 + 55x + 17x2 = 0 Solving 180 + 55x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 10.58823529 + 3.235294118x + x2 = 0 Move the constant term to the right: Add '-10.58823529' to each side of the equation. 10.58823529 + 3.235294118x + -10.58823529 + x2 = 0 + -10.58823529 Reorder the terms: 10.58823529 + -10.58823529 + 3.235294118x + x2 = 0 + -10.58823529 Combine like terms: 10.58823529 + -10.58823529 = 0.00000000 0.00000000 + 3.235294118x + x2 = 0 + -10.58823529 3.235294118x + x2 = 0 + -10.58823529 Combine like terms: 0 + -10.58823529 = -10.58823529 3.235294118x + x2 = -10.58823529 The x term is 3.235294118x. Take half its coefficient (1.617647059). Square it (2.616782007) and add it to both sides. Add '2.616782007' to each side of the equation. 3.235294118x + 2.616782007 + x2 = -10.58823529 + 2.616782007 Reorder the terms: 2.616782007 + 3.235294118x + x2 = -10.58823529 + 2.616782007 Combine like terms: -10.58823529 + 2.616782007 = -7.971453283 2.616782007 + 3.235294118x + x2 = -7.971453283 Factor a perfect square on the left side: (x + 1.617647059)(x + 1.617647059) = -7.971453283 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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