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Simplifying 7x2 + -5x + 11 = 243 Reorder the terms: 11 + -5x + 7x2 = 243 Solving 11 + -5x + 7x2 = 243 Solving for variable 'x'. Reorder the terms: 11 + -243 + -5x + 7x2 = 243 + -243 Combine like terms: 11 + -243 = -232 -232 + -5x + 7x2 = 243 + -243 Combine like terms: 243 + -243 = 0 -232 + -5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -33.14285714 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '33.14285714' to each side of the equation. -33.14285714 + -0.7142857143x + 33.14285714 + x2 = 0 + 33.14285714 Reorder the terms: -33.14285714 + 33.14285714 + -0.7142857143x + x2 = 0 + 33.14285714 Combine like terms: -33.14285714 + 33.14285714 = 0.00000000 0.00000000 + -0.7142857143x + x2 = 0 + 33.14285714 -0.7142857143x + x2 = 0 + 33.14285714 Combine like terms: 0 + 33.14285714 = 33.14285714 -0.7142857143x + x2 = 33.14285714 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 = 33.14285714 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 33.14285714 + 0.1275510204 Combine like terms: 33.14285714 + 0.1275510204 = 33.2704081604 0.1275510204 + -0.7142857143x + x2 = 33.2704081604 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 33.2704081604 Calculate the square root of the right side: 5.768050638 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 5.768050638 and -5.768050638.Subproblem 1
x + -0.3571428572 = 5.768050638 Simplifying x + -0.3571428572 = 5.768050638 Reorder the terms: -0.3571428572 + x = 5.768050638 Solving -0.3571428572 + x = 5.768050638 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 = 5.768050638 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 5.768050638 + 0.3571428572 x = 5.768050638 + 0.3571428572 Combine like terms: 5.768050638 + 0.3571428572 = 6.1251934952 x = 6.1251934952 Simplifying x = 6.1251934952Subproblem 2
x + -0.3571428572 = -5.768050638 Simplifying x + -0.3571428572 = -5.768050638 Reorder the terms: -0.3571428572 + x = -5.768050638 Solving -0.3571428572 + x = -5.768050638 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 = -5.768050638 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -5.768050638 + 0.3571428572 x = -5.768050638 + 0.3571428572 Combine like terms: -5.768050638 + 0.3571428572 = -5.4109077808 x = -5.4109077808 Simplifying x = -5.4109077808Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.1251934952, -5.4109077808}
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