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Simplifying 26x2 + -600x + 3600 = 0 Reorder the terms: 3600 + -600x + 26x2 = 0 Solving 3600 + -600x + 26x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1800 + -300x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1800 + -300x + 13x2)' equal to zero and attempt to solve: Simplifying 1800 + -300x + 13x2 = 0 Solving 1800 + -300x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 138.4615385 + -23.07692308x + x2 = 0 Move the constant term to the right: Add '-138.4615385' to each side of the equation. 138.4615385 + -23.07692308x + -138.4615385 + x2 = 0 + -138.4615385 Reorder the terms: 138.4615385 + -138.4615385 + -23.07692308x + x2 = 0 + -138.4615385 Combine like terms: 138.4615385 + -138.4615385 = 0.0000000 0.0000000 + -23.07692308x + x2 = 0 + -138.4615385 -23.07692308x + x2 = 0 + -138.4615385 Combine like terms: 0 + -138.4615385 = -138.4615385 -23.07692308x + x2 = -138.4615385 The x term is -23.07692308x. Take half its coefficient (-11.53846154). Square it (133.1360947) and add it to both sides. Add '133.1360947' to each side of the equation. -23.07692308x + 133.1360947 + x2 = -138.4615385 + 133.1360947 Reorder the terms: 133.1360947 + -23.07692308x + x2 = -138.4615385 + 133.1360947 Combine like terms: -138.4615385 + 133.1360947 = -5.3254438 133.1360947 + -23.07692308x + x2 = -5.3254438 Factor a perfect square on the left side: (x + -11.53846154)(x + -11.53846154) = -5.3254438 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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