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Simplifying 42x2 + 22x = 9 Reorder the terms: 22x + 42x2 = 9 Solving 22x + 42x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 22x + 42x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 22x + 42x2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -0.2142857143 + 0.5238095238x + x2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.5238095238x + 0.2142857143 + x2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + 0.5238095238x + x2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + 0.5238095238x + x2 = 0 + 0.2142857143 0.5238095238x + x2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 0.5238095238x + x2 = 0.2142857143 The x term is 0.5238095238x. Take half its coefficient (0.2619047619). Square it (0.06859410431) and add it to both sides. Add '0.06859410431' to each side of the equation. 0.5238095238x + 0.06859410431 + x2 = 0.2142857143 + 0.06859410431 Reorder the terms: 0.06859410431 + 0.5238095238x + x2 = 0.2142857143 + 0.06859410431 Combine like terms: 0.2142857143 + 0.06859410431 = 0.28287981861 0.06859410431 + 0.5238095238x + x2 = 0.28287981861 Factor a perfect square on the left side: (x + 0.2619047619)(x + 0.2619047619) = 0.28287981861 Calculate the square root of the right side: 0.531864474 Break this problem into two subproblems by setting (x + 0.2619047619) equal to 0.531864474 and -0.531864474.Subproblem 1
x + 0.2619047619 = 0.531864474 Simplifying x + 0.2619047619 = 0.531864474 Reorder the terms: 0.2619047619 + x = 0.531864474 Solving 0.2619047619 + x = 0.531864474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2619047619' to each side of the equation. 0.2619047619 + -0.2619047619 + x = 0.531864474 + -0.2619047619 Combine like terms: 0.2619047619 + -0.2619047619 = 0.0000000000 0.0000000000 + x = 0.531864474 + -0.2619047619 x = 0.531864474 + -0.2619047619 Combine like terms: 0.531864474 + -0.2619047619 = 0.2699597121 x = 0.2699597121 Simplifying x = 0.2699597121Subproblem 2
x + 0.2619047619 = -0.531864474 Simplifying x + 0.2619047619 = -0.531864474 Reorder the terms: 0.2619047619 + x = -0.531864474 Solving 0.2619047619 + x = -0.531864474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2619047619' to each side of the equation. 0.2619047619 + -0.2619047619 + x = -0.531864474 + -0.2619047619 Combine like terms: 0.2619047619 + -0.2619047619 = 0.0000000000 0.0000000000 + x = -0.531864474 + -0.2619047619 x = -0.531864474 + -0.2619047619 Combine like terms: -0.531864474 + -0.2619047619 = -0.7937692359 x = -0.7937692359 Simplifying x = -0.7937692359Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2699597121, -0.7937692359}
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