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Simplifying 2x + -454 = x(65x + 85) Reorder the terms: -454 + 2x = x(65x + 85) Reorder the terms: -454 + 2x = x(85 + 65x) -454 + 2x = (85 * x + 65x * x) -454 + 2x = (85x + 65x2) Solving -454 + 2x = 85x + 65x2 Solving for variable 'x'. Combine like terms: 2x + -85x = -83x -454 + -83x + -65x2 = 85x + 65x2 + -85x + -65x2 Reorder the terms: -454 + -83x + -65x2 = 85x + -85x + 65x2 + -65x2 Combine like terms: 85x + -85x = 0 -454 + -83x + -65x2 = 0 + 65x2 + -65x2 -454 + -83x + -65x2 = 65x2 + -65x2 Combine like terms: 65x2 + -65x2 = 0 -454 + -83x + -65x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(454 + 83x + 65x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(454 + 83x + 65x2)' equal to zero and attempt to solve: Simplifying 454 + 83x + 65x2 = 0 Solving 454 + 83x + 65x2 = 0 Begin completing the square. Divide all terms by 65 the coefficient of the squared term: Divide each side by '65'. 6.984615385 + 1.276923077x + x2 = 0 Move the constant term to the right: Add '-6.984615385' to each side of the equation. 6.984615385 + 1.276923077x + -6.984615385 + x2 = 0 + -6.984615385 Reorder the terms: 6.984615385 + -6.984615385 + 1.276923077x + x2 = 0 + -6.984615385 Combine like terms: 6.984615385 + -6.984615385 = 0.000000000 0.000000000 + 1.276923077x + x2 = 0 + -6.984615385 1.276923077x + x2 = 0 + -6.984615385 Combine like terms: 0 + -6.984615385 = -6.984615385 1.276923077x + x2 = -6.984615385 The x term is 1.276923077x. Take half its coefficient (0.6384615385). Square it (0.4076331361) and add it to both sides. Add '0.4076331361' to each side of the equation. 1.276923077x + 0.4076331361 + x2 = -6.984615385 + 0.4076331361 Reorder the terms: 0.4076331361 + 1.276923077x + x2 = -6.984615385 + 0.4076331361 Combine like terms: -6.984615385 + 0.4076331361 = -6.5769822489 0.4076331361 + 1.276923077x + x2 = -6.5769822489 Factor a perfect square on the left side: (x + 0.6384615385)(x + 0.6384615385) = -6.5769822489 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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