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Simplifying 0.33x2 + 0.71x + -0.14 = 0 Reorder the terms: -0.14 + 0.71x + 0.33x2 = 0 Solving -0.14 + 0.71x + 0.33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.33 the coefficient of the squared term: Divide each side by '0.33'. -0.4242424242 + 2.151515152x + x2 = 0 Move the constant term to the right: Add '0.4242424242' to each side of the equation. -0.4242424242 + 2.151515152x + 0.4242424242 + x2 = 0 + 0.4242424242 Reorder the terms: -0.4242424242 + 0.4242424242 + 2.151515152x + x2 = 0 + 0.4242424242 Combine like terms: -0.4242424242 + 0.4242424242 = 0.0000000000 0.0000000000 + 2.151515152x + x2 = 0 + 0.4242424242 2.151515152x + x2 = 0 + 0.4242424242 Combine like terms: 0 + 0.4242424242 = 0.4242424242 2.151515152x + x2 = 0.4242424242 The x term is 2.151515152x. Take half its coefficient (1.075757576). Square it (1.157254362) and add it to both sides. Add '1.157254362' to each side of the equation. 2.151515152x + 1.157254362 + x2 = 0.4242424242 + 1.157254362 Reorder the terms: 1.157254362 + 2.151515152x + x2 = 0.4242424242 + 1.157254362 Combine like terms: 0.4242424242 + 1.157254362 = 1.5814967862 1.157254362 + 2.151515152x + x2 = 1.5814967862 Factor a perfect square on the left side: (x + 1.075757576)(x + 1.075757576) = 1.5814967862 Calculate the square root of the right side: 1.257575758 Break this problem into two subproblems by setting (x + 1.075757576) equal to 1.257575758 and -1.257575758.Subproblem 1
x + 1.075757576 = 1.257575758 Simplifying x + 1.075757576 = 1.257575758 Reorder the terms: 1.075757576 + x = 1.257575758 Solving 1.075757576 + x = 1.257575758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.075757576' to each side of the equation. 1.075757576 + -1.075757576 + x = 1.257575758 + -1.075757576 Combine like terms: 1.075757576 + -1.075757576 = 0.000000000 0.000000000 + x = 1.257575758 + -1.075757576 x = 1.257575758 + -1.075757576 Combine like terms: 1.257575758 + -1.075757576 = 0.181818182 x = 0.181818182 Simplifying x = 0.181818182Subproblem 2
x + 1.075757576 = -1.257575758 Simplifying x + 1.075757576 = -1.257575758 Reorder the terms: 1.075757576 + x = -1.257575758 Solving 1.075757576 + x = -1.257575758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.075757576' to each side of the equation. 1.075757576 + -1.075757576 + x = -1.257575758 + -1.075757576 Combine like terms: 1.075757576 + -1.075757576 = 0.000000000 0.000000000 + x = -1.257575758 + -1.075757576 x = -1.257575758 + -1.075757576 Combine like terms: -1.257575758 + -1.075757576 = -2.333333334 x = -2.333333334 Simplifying x = -2.333333334Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.181818182, -2.333333334}
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