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Simplifying 7x2 + 5x = 5 Reorder the terms: 5x + 7x2 = 5 Solving 5x + 7x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 5x + 7x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 0.7142857143x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 0.7142857143x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 0.7142857143x + x2 = 0 + 0.7142857143 0.7142857143x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 0.7142857143x + x2 = 0.7142857143 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 = 0.7142857143 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 0.7142857143 + 0.1275510204 Combine like terms: 0.7142857143 + 0.1275510204 = 0.8418367347 0.1275510204 + 0.7142857143x + x2 = 0.8418367347 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 0.8418367347 Calculate the square root of the right side: 0.917516613 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 0.917516613 and -0.917516613.Subproblem 1
x + 0.3571428572 = 0.917516613 Simplifying x + 0.3571428572 = 0.917516613 Reorder the terms: 0.3571428572 + x = 0.917516613 Solving 0.3571428572 + x = 0.917516613 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 = 0.917516613 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 0.917516613 + -0.3571428572 x = 0.917516613 + -0.3571428572 Combine like terms: 0.917516613 + -0.3571428572 = 0.5603737558 x = 0.5603737558 Simplifying x = 0.5603737558Subproblem 2
x + 0.3571428572 = -0.917516613 Simplifying x + 0.3571428572 = -0.917516613 Reorder the terms: 0.3571428572 + x = -0.917516613 Solving 0.3571428572 + x = -0.917516613 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 = -0.917516613 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -0.917516613 + -0.3571428572 x = -0.917516613 + -0.3571428572 Combine like terms: -0.917516613 + -0.3571428572 = -1.2746594702 x = -1.2746594702 Simplifying x = -1.2746594702Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5603737558, -1.2746594702}
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