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Simplifying 45x2 + 5(x + 34) = 0 Reorder the terms: 45x2 + 5(34 + x) = 0 45x2 + (34 * 5 + x * 5) = 0 45x2 + (170 + 5x) = 0 Reorder the terms: 170 + 5x + 45x2 = 0 Solving 170 + 5x + 45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(34 + x + 9x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(34 + x + 9x2)' equal to zero and attempt to solve: Simplifying 34 + x + 9x2 = 0 Solving 34 + x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 3.777777778 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '-3.777777778' to each side of the equation. 3.777777778 + 0.1111111111x + -3.777777778 + x2 = 0 + -3.777777778 Reorder the terms: 3.777777778 + -3.777777778 + 0.1111111111x + x2 = 0 + -3.777777778 Combine like terms: 3.777777778 + -3.777777778 = 0.000000000 0.000000000 + 0.1111111111x + x2 = 0 + -3.777777778 0.1111111111x + x2 = 0 + -3.777777778 Combine like terms: 0 + -3.777777778 = -3.777777778 0.1111111111x + x2 = -3.777777778 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1111111111x + 0.25 + x2 = -3.777777778 + 0.25 Reorder the terms: 0.25 + 0.1111111111x + x2 = -3.777777778 + 0.25 Combine like terms: -3.777777778 + 0.25 = -3.527777778 0.25 + 0.1111111111x + x2 = -3.527777778 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -3.527777778 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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