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Simplifying 7x2 + -5x + 11 = 343 Reorder the terms: 11 + -5x + 7x2 = 343 Solving 11 + -5x + 7x2 = 343 Solving for variable 'x'. Reorder the terms: 11 + -343 + -5x + 7x2 = 343 + -343 Combine like terms: 11 + -343 = -332 -332 + -5x + 7x2 = 343 + -343 Combine like terms: 343 + -343 = 0 -332 + -5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -47.42857143 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '47.42857143' to each side of the equation. -47.42857143 + -0.7142857143x + 47.42857143 + x2 = 0 + 47.42857143 Reorder the terms: -47.42857143 + 47.42857143 + -0.7142857143x + x2 = 0 + 47.42857143 Combine like terms: -47.42857143 + 47.42857143 = 0.00000000 0.00000000 + -0.7142857143x + x2 = 0 + 47.42857143 -0.7142857143x + x2 = 0 + 47.42857143 Combine like terms: 0 + 47.42857143 = 47.42857143 -0.7142857143x + x2 = 47.42857143 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 = 47.42857143 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 47.42857143 + 0.1275510204 Combine like terms: 47.42857143 + 0.1275510204 = 47.5561224504 0.1275510204 + -0.7142857143x + x2 = 47.5561224504 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 47.5561224504 Calculate the square root of the right side: 6.896094725 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 6.896094725 and -6.896094725.Subproblem 1
x + -0.3571428572 = 6.896094725 Simplifying x + -0.3571428572 = 6.896094725 Reorder the terms: -0.3571428572 + x = 6.896094725 Solving -0.3571428572 + x = 6.896094725 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 = 6.896094725 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 6.896094725 + 0.3571428572 x = 6.896094725 + 0.3571428572 Combine like terms: 6.896094725 + 0.3571428572 = 7.2532375822 x = 7.2532375822 Simplifying x = 7.2532375822Subproblem 2
x + -0.3571428572 = -6.896094725 Simplifying x + -0.3571428572 = -6.896094725 Reorder the terms: -0.3571428572 + x = -6.896094725 Solving -0.3571428572 + x = -6.896094725 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 = -6.896094725 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -6.896094725 + 0.3571428572 x = -6.896094725 + 0.3571428572 Combine like terms: -6.896094725 + 0.3571428572 = -6.5389518678 x = -6.5389518678 Simplifying x = -6.5389518678Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.2532375822, -6.5389518678}
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