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Simplifying 180 + -1x = 45(x + -2x2) 180 + -1x = (x * 45 + -2x2 * 45) 180 + -1x = (45x + -90x2) Solving 180 + -1x = 45x + -90x2 Solving for variable 'x'. Combine like terms: -1x + -45x = -46x 180 + -46x + 90x2 = 45x + -90x2 + -45x + 90x2 Reorder the terms: 180 + -46x + 90x2 = 45x + -45x + -90x2 + 90x2 Combine like terms: 45x + -45x = 0 180 + -46x + 90x2 = 0 + -90x2 + 90x2 180 + -46x + 90x2 = -90x2 + 90x2 Combine like terms: -90x2 + 90x2 = 0 180 + -46x + 90x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(90 + -23x + 45x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(90 + -23x + 45x2)' equal to zero and attempt to solve: Simplifying 90 + -23x + 45x2 = 0 Solving 90 + -23x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. 2 + -0.5111111111x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -0.5111111111x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -0.5111111111x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -0.5111111111x + x2 = 0 + -2 -0.5111111111x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -0.5111111111x + x2 = -2 The x term is -0.5111111111x. Take half its coefficient (-0.2555555556). Square it (0.06530864200) and add it to both sides. Add '0.06530864200' to each side of the equation. -0.5111111111x + 0.06530864200 + x2 = -2 + 0.06530864200 Reorder the terms: 0.06530864200 + -0.5111111111x + x2 = -2 + 0.06530864200 Combine like terms: -2 + 0.06530864200 = -1.934691358 0.06530864200 + -0.5111111111x + x2 = -1.934691358 Factor a perfect square on the left side: (x + -0.2555555556)(x + -0.2555555556) = -1.934691358 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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