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Simplifying 5x2 + 22x + -21 = 0 Reorder the terms: -21 + 22x + 5x2 = 0 Solving -21 + 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'. -4.2 + 4.4x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 4.4x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 4.4x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 4.4x + x2 = 0 + 4.2 4.4x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 4.4x + x2 = 4.2 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 = 4.2 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = 4.2 + 4.84 Combine like terms: 4.2 + 4.84 = 9.04 4.84 + 4.4x + x2 = 9.04 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = 9.04 Calculate the square root of the right side: 3.006659276 Break this problem into two subproblems by setting (x + 2.2) equal to 3.006659276 and -3.006659276.Subproblem 1
x + 2.2 = 3.006659276 Simplifying x + 2.2 = 3.006659276 Reorder the terms: 2.2 + x = 3.006659276 Solving 2.2 + x = 3.006659276 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 = 3.006659276 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 3.006659276 + -2.2 x = 3.006659276 + -2.2 Combine like terms: 3.006659276 + -2.2 = 0.806659276 x = 0.806659276 Simplifying x = 0.806659276Subproblem 2
x + 2.2 = -3.006659276 Simplifying x + 2.2 = -3.006659276 Reorder the terms: 2.2 + x = -3.006659276 Solving 2.2 + x = -3.006659276 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 = -3.006659276 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -3.006659276 + -2.2 x = -3.006659276 + -2.2 Combine like terms: -3.006659276 + -2.2 = -5.206659276 x = -5.206659276 Simplifying x = -5.206659276Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.806659276, -5.206659276}
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