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Simplifying 7x2 = x + 1 Reorder the terms: 7x2 = 1 + x Solving 7x2 = 1 + x Solving for variable 'x'. Reorder the terms: -1 + -1x + 7x2 = 1 + x + -1 + -1x Reorder the terms: -1 + -1x + 7x2 = 1 + -1 + x + -1x Combine like terms: 1 + -1 = 0 -1 + -1x + 7x2 = 0 + x + -1x -1 + -1x + 7x2 = x + -1x Combine like terms: x + -1x = 0 -1 + -1x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.1428571429x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.1428571429x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.1428571429x + x2 = 0 + 0.1428571429 -0.1428571429x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.1428571429x + x2 = 0.1428571429 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = 0.1428571429 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 0.1428571429 + 0.005102040819 Combine like terms: 0.1428571429 + 0.005102040819 = 0.147959183719 0.005102040819 + -0.1428571429x + x2 = 0.147959183719 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 0.147959183719 Calculate the square root of the right side: 0.384654629 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 0.384654629 and -0.384654629.Subproblem 1
x + -0.07142857145 = 0.384654629 Simplifying x + -0.07142857145 = 0.384654629 Reorder the terms: -0.07142857145 + x = 0.384654629 Solving -0.07142857145 + x = 0.384654629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 0.384654629 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.384654629 + 0.07142857145 x = 0.384654629 + 0.07142857145 Combine like terms: 0.384654629 + 0.07142857145 = 0.45608320045 x = 0.45608320045 Simplifying x = 0.45608320045Subproblem 2
x + -0.07142857145 = -0.384654629 Simplifying x + -0.07142857145 = -0.384654629 Reorder the terms: -0.07142857145 + x = -0.384654629 Solving -0.07142857145 + x = -0.384654629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -0.384654629 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.384654629 + 0.07142857145 x = -0.384654629 + 0.07142857145 Combine like terms: -0.384654629 + 0.07142857145 = -0.31322605755 x = -0.31322605755 Simplifying x = -0.31322605755Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.45608320045, -0.31322605755}
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