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Simplifying 5.71428571429 = x2 + x Reorder the terms: 5.71428571429 = x + x2 Solving 5.71428571429 = x + x2 Solving for variable 'x'. Reorder the terms: 5.71428571429 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 5.71428571429 + -1x + -1x2 = 0 + x2 + -1x2 5.71428571429 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5.71428571429 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5.714285714 + x + x2 = 0 Move the constant term to the right: Add '5.714285714' to each side of the equation. -5.714285714 + x + 5.714285714 + x2 = 0 + 5.714285714 Reorder the terms: -5.714285714 + 5.714285714 + x + x2 = 0 + 5.714285714 Combine like terms: -5.714285714 + 5.714285714 = 0.000000000 0.000000000 + x + x2 = 0 + 5.714285714 x + x2 = 0 + 5.714285714 Combine like terms: 0 + 5.714285714 = 5.714285714 x + x2 = 5.714285714 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 5.714285714 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 5.714285714 + 0.25 Combine like terms: 5.714285714 + 0.25 = 5.964285714 1.25 + x2 = 5.964285714 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5.964285714 Calculate the square root of the right side: 2.442188714 Break this problem into two subproblems by setting (x + 0.5) equal to 2.442188714 and -2.442188714.Subproblem 1
x + 0.5 = 2.442188714 Simplifying x + 0.5 = 2.442188714 Reorder the terms: 0.5 + x = 2.442188714 Solving 0.5 + x = 2.442188714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.442188714 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.442188714 + -0.5 x = 2.442188714 + -0.5 Combine like terms: 2.442188714 + -0.5 = 1.942188714 x = 1.942188714 Simplifying x = 1.942188714Subproblem 2
x + 0.5 = -2.442188714 Simplifying x + 0.5 = -2.442188714 Reorder the terms: 0.5 + x = -2.442188714 Solving 0.5 + x = -2.442188714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.442188714 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.442188714 + -0.5 x = -2.442188714 + -0.5 Combine like terms: -2.442188714 + -0.5 = -2.942188714 x = -2.942188714 Simplifying x = -2.942188714Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.942188714, -2.942188714}
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