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Simplifying 7x(x + 1) = 2x + 57 Reorder the terms: 7x(1 + x) = 2x + 57 (1 * 7x + x * 7x) = 2x + 57 (7x + 7x2) = 2x + 57 Reorder the terms: 7x + 7x2 = 57 + 2x Solving 7x + 7x2 = 57 + 2x Solving for variable 'x'. Reorder the terms: -57 + 7x + -2x + 7x2 = 57 + 2x + -57 + -2x Combine like terms: 7x + -2x = 5x -57 + 5x + 7x2 = 57 + 2x + -57 + -2x Reorder the terms: -57 + 5x + 7x2 = 57 + -57 + 2x + -2x Combine like terms: 57 + -57 = 0 -57 + 5x + 7x2 = 0 + 2x + -2x -57 + 5x + 7x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -57 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -8.142857143 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '8.142857143' to each side of the equation. -8.142857143 + 0.7142857143x + 8.142857143 + x2 = 0 + 8.142857143 Reorder the terms: -8.142857143 + 8.142857143 + 0.7142857143x + x2 = 0 + 8.142857143 Combine like terms: -8.142857143 + 8.142857143 = 0.000000000 0.000000000 + 0.7142857143x + x2 = 0 + 8.142857143 0.7142857143x + x2 = 0 + 8.142857143 Combine like terms: 0 + 8.142857143 = 8.142857143 0.7142857143x + x2 = 8.142857143 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = 8.142857143 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 8.142857143 + 0.1275510204 Combine like terms: 8.142857143 + 0.1275510204 = 8.2704081634 0.1275510204 + 0.7142857143x + x2 = 8.2704081634 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 8.2704081634 Calculate the square root of the right side: 2.875831734 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 2.875831734 and -2.875831734.Subproblem 1
x + 0.3571428572 = 2.875831734 Simplifying x + 0.3571428572 = 2.875831734 Reorder the terms: 0.3571428572 + x = 2.875831734 Solving 0.3571428572 + x = 2.875831734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 2.875831734 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 2.875831734 + -0.3571428572 x = 2.875831734 + -0.3571428572 Combine like terms: 2.875831734 + -0.3571428572 = 2.5186888768 x = 2.5186888768 Simplifying x = 2.5186888768Subproblem 2
x + 0.3571428572 = -2.875831734 Simplifying x + 0.3571428572 = -2.875831734 Reorder the terms: 0.3571428572 + x = -2.875831734 Solving 0.3571428572 + x = -2.875831734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -2.875831734 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -2.875831734 + -0.3571428572 x = -2.875831734 + -0.3571428572 Combine like terms: -2.875831734 + -0.3571428572 = -3.2329745912 x = -3.2329745912 Simplifying x = -3.2329745912Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5186888768, -3.2329745912}
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