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Simplifying 19X4 + 27X2 = 3.6 Reorder the terms: 27X2 + 19X4 = 3.6 Solving 27X2 + 19X4 = 3.6 Solving for variable 'X'. Reorder the terms: -3.6 + 27X2 + 19X4 = 3.6 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 -3.6 + 27X2 + 19X4 = 0.0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.1894736842 + 1.421052632X2 + X4 = 0.0 Move the constant term to the right: Add '0.1894736842' to each side of the equation. -0.1894736842 + 1.421052632X2 + 0.1894736842 + X4 = 0.0 + 0.1894736842 Reorder the terms: -0.1894736842 + 0.1894736842 + 1.421052632X2 + X4 = 0.0 + 0.1894736842 Combine like terms: -0.1894736842 + 0.1894736842 = 0.0000000000 0.0000000000 + 1.421052632X2 + X4 = 0.0 + 0.1894736842 1.421052632X2 + X4 = 0.0 + 0.1894736842 Combine like terms: 0.0 + 0.1894736842 = 0.1894736842 1.421052632X2 + X4 = 0.1894736842 The X term is 1.421052632X2. Take half its coefficient (0.710526316). Square it (0.5048476457) and add it to both sides. Add '0.5048476457' to each side of the equation. 1.421052632X2 + 0.5048476457 + X4 = 0.1894736842 + 0.5048476457 Reorder the terms: 0.5048476457 + 1.421052632X2 + X4 = 0.1894736842 + 0.5048476457 Combine like terms: 0.1894736842 + 0.5048476457 = 0.6943213299 0.5048476457 + 1.421052632X2 + X4 = 0.6943213299 Factor a perfect square on the left side: (X2 + 0.710526316)(X2 + 0.710526316) = 0.6943213299 Calculate the square root of the right side: 0.833259461 Break this problem into two subproblems by setting (X2 + 0.710526316) equal to 0.833259461 and -0.833259461.Subproblem 1
X2 + 0.710526316 = 0.833259461 Simplifying X2 + 0.710526316 = 0.833259461 Reorder the terms: 0.710526316 + X2 = 0.833259461 Solving 0.710526316 + X2 = 0.833259461 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.710526316' to each side of the equation. 0.710526316 + -0.710526316 + X2 = 0.833259461 + -0.710526316 Combine like terms: 0.710526316 + -0.710526316 = 0.000000000 0.000000000 + X2 = 0.833259461 + -0.710526316 X2 = 0.833259461 + -0.710526316 Combine like terms: 0.833259461 + -0.710526316 = 0.122733145 X2 = 0.122733145 Simplifying X2 = 0.122733145 Take the square root of each side: X = {-0.350332906, 0.350332906}Subproblem 2
X2 + 0.710526316 = -0.833259461 Simplifying X2 + 0.710526316 = -0.833259461 Reorder the terms: 0.710526316 + X2 = -0.833259461 Solving 0.710526316 + X2 = -0.833259461 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.710526316' to each side of the equation. 0.710526316 + -0.710526316 + X2 = -0.833259461 + -0.710526316 Combine like terms: 0.710526316 + -0.710526316 = 0.000000000 0.000000000 + X2 = -0.833259461 + -0.710526316 X2 = -0.833259461 + -0.710526316 Combine like terms: -0.833259461 + -0.710526316 = -1.543785777 X2 = -1.543785777 Simplifying X2 = -1.543785777 Reorder the terms: 1.543785777 + X2 = -1.543785777 + 1.543785777 Combine like terms: -1.543785777 + 1.543785777 = 0.000000000 1.543785777 + X2 = 0.000000000 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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