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Simplifying 5x2 + 33x + 22 = 0 Reorder the terms: 22 + 33x + 5x2 = 0 Solving 22 + 33x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.4 + 6.6x + x2 = 0 Move the constant term to the right: Add '-4.4' to each side of the equation. 4.4 + 6.6x + -4.4 + x2 = 0 + -4.4 Reorder the terms: 4.4 + -4.4 + 6.6x + x2 = 0 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + 6.6x + x2 = 0 + -4.4 6.6x + x2 = 0 + -4.4 Combine like terms: 0 + -4.4 = -4.4 6.6x + x2 = -4.4 The x term is 6.6x. Take half its coefficient (3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. 6.6x + 10.89 + x2 = -4.4 + 10.89 Reorder the terms: 10.89 + 6.6x + x2 = -4.4 + 10.89 Combine like terms: -4.4 + 10.89 = 6.49 10.89 + 6.6x + x2 = 6.49 Factor a perfect square on the left side: (x + 3.3)(x + 3.3) = 6.49 Calculate the square root of the right side: 2.547547841 Break this problem into two subproblems by setting (x + 3.3) equal to 2.547547841 and -2.547547841.Subproblem 1
x + 3.3 = 2.547547841 Simplifying x + 3.3 = 2.547547841 Reorder the terms: 3.3 + x = 2.547547841 Solving 3.3 + x = 2.547547841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + x = 2.547547841 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + x = 2.547547841 + -3.3 x = 2.547547841 + -3.3 Combine like terms: 2.547547841 + -3.3 = -0.752452159 x = -0.752452159 Simplifying x = -0.752452159Subproblem 2
x + 3.3 = -2.547547841 Simplifying x + 3.3 = -2.547547841 Reorder the terms: 3.3 + x = -2.547547841 Solving 3.3 + x = -2.547547841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.3' to each side of the equation. 3.3 + -3.3 + x = -2.547547841 + -3.3 Combine like terms: 3.3 + -3.3 = 0.0 0.0 + x = -2.547547841 + -3.3 x = -2.547547841 + -3.3 Combine like terms: -2.547547841 + -3.3 = -5.847547841 x = -5.847547841 Simplifying x = -5.847547841Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.752452159, -5.847547841}
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