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Simplifying -23x + -12x2 = 45 Solving -23x + -12x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -23x + -12x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -23x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(45 + 23x + 12x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(45 + 23x + 12x2)' equal to zero and attempt to solve: Simplifying 45 + 23x + 12x2 = 0 Solving 45 + 23x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 3.75 + 1.916666667x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 1.916666667x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 1.916666667x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 1.916666667x + x2 = 0 + -3.75 1.916666667x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 1.916666667x + x2 = -3.75 The x term is 1.916666667x. Take half its coefficient (0.9583333335). Square it (0.9184027781) and add it to both sides. Add '0.9184027781' to each side of the equation. 1.916666667x + 0.9184027781 + x2 = -3.75 + 0.9184027781 Reorder the terms: 0.9184027781 + 1.916666667x + x2 = -3.75 + 0.9184027781 Combine like terms: -3.75 + 0.9184027781 = -2.8315972219 0.9184027781 + 1.916666667x + x2 = -2.8315972219 Factor a perfect square on the left side: (x + 0.9583333335)(x + 0.9583333335) = -2.8315972219 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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