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Simplifying 5x2 + 22x + 11 = 0 Reorder the terms: 11 + 22x + 5x2 = 0 Solving 11 + 22x + 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'. 2.2 + 4.4x + x2 = 0 Move the constant term to the right: Add '-2.2' to each side of the equation. 2.2 + 4.4x + -2.2 + x2 = 0 + -2.2 Reorder the terms: 2.2 + -2.2 + 4.4x + x2 = 0 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + 4.4x + x2 = 0 + -2.2 4.4x + x2 = 0 + -2.2 Combine like terms: 0 + -2.2 = -2.2 4.4x + x2 = -2.2 The x term is 4.4x. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4x + 4.84 + x2 = -2.2 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = -2.2 + 4.84 Combine like terms: -2.2 + 4.84 = 2.64 4.84 + 4.4x + x2 = 2.64 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = 2.64 Calculate the square root of the right side: 1.624807681 Break this problem into two subproblems by setting (x + 2.2) equal to 1.624807681 and -1.624807681.Subproblem 1
x + 2.2 = 1.624807681 Simplifying x + 2.2 = 1.624807681 Reorder the terms: 2.2 + x = 1.624807681 Solving 2.2 + x = 1.624807681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = 1.624807681 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 1.624807681 + -2.2 x = 1.624807681 + -2.2 Combine like terms: 1.624807681 + -2.2 = -0.575192319 x = -0.575192319 Simplifying x = -0.575192319Subproblem 2
x + 2.2 = -1.624807681 Simplifying x + 2.2 = -1.624807681 Reorder the terms: 2.2 + x = -1.624807681 Solving 2.2 + x = -1.624807681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = -1.624807681 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -1.624807681 + -2.2 x = -1.624807681 + -2.2 Combine like terms: -1.624807681 + -2.2 = -3.824807681 x = -3.824807681 Simplifying x = -3.824807681Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.575192319, -3.824807681}
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