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Simplifying 39x2 + -88x + -56 = 0 Reorder the terms: -56 + -88x + 39x2 = 0 Solving -56 + -88x + 39x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 39 the coefficient of the squared term: Divide each side by '39'. -1.435897436 + -2.256410256x + x2 = 0 Move the constant term to the right: Add '1.435897436' to each side of the equation. -1.435897436 + -2.256410256x + 1.435897436 + x2 = 0 + 1.435897436 Reorder the terms: -1.435897436 + 1.435897436 + -2.256410256x + x2 = 0 + 1.435897436 Combine like terms: -1.435897436 + 1.435897436 = 0.000000000 0.000000000 + -2.256410256x + x2 = 0 + 1.435897436 -2.256410256x + x2 = 0 + 1.435897436 Combine like terms: 0 + 1.435897436 = 1.435897436 -2.256410256x + x2 = 1.435897436 The x term is -2.256410256x. Take half its coefficient (-1.128205128). Square it (1.272846811) and add it to both sides. Add '1.272846811' to each side of the equation. -2.256410256x + 1.272846811 + x2 = 1.435897436 + 1.272846811 Reorder the terms: 1.272846811 + -2.256410256x + x2 = 1.435897436 + 1.272846811 Combine like terms: 1.435897436 + 1.272846811 = 2.708744247 1.272846811 + -2.256410256x + x2 = 2.708744247 Factor a perfect square on the left side: (x + -1.128205128)(x + -1.128205128) = 2.708744247 Calculate the square root of the right side: 1.645826311 Break this problem into two subproblems by setting (x + -1.128205128) equal to 1.645826311 and -1.645826311.Subproblem 1
x + -1.128205128 = 1.645826311 Simplifying x + -1.128205128 = 1.645826311 Reorder the terms: -1.128205128 + x = 1.645826311 Solving -1.128205128 + x = 1.645826311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.128205128' to each side of the equation. -1.128205128 + 1.128205128 + x = 1.645826311 + 1.128205128 Combine like terms: -1.128205128 + 1.128205128 = 0.000000000 0.000000000 + x = 1.645826311 + 1.128205128 x = 1.645826311 + 1.128205128 Combine like terms: 1.645826311 + 1.128205128 = 2.774031439 x = 2.774031439 Simplifying x = 2.774031439Subproblem 2
x + -1.128205128 = -1.645826311 Simplifying x + -1.128205128 = -1.645826311 Reorder the terms: -1.128205128 + x = -1.645826311 Solving -1.128205128 + x = -1.645826311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.128205128' to each side of the equation. -1.128205128 + 1.128205128 + x = -1.645826311 + 1.128205128 Combine like terms: -1.128205128 + 1.128205128 = 0.000000000 0.000000000 + x = -1.645826311 + 1.128205128 x = -1.645826311 + 1.128205128 Combine like terms: -1.645826311 + 1.128205128 = -0.517621183 x = -0.517621183 Simplifying x = -0.517621183Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.774031439, -0.517621183}
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