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Simplifying 20x + x2 = 122 Solving 20x + x2 = 122 Solving for variable 'x'. Reorder the terms: -122 + 20x + x2 = 122 + -122 Combine like terms: 122 + -122 = 0 -122 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '122' to each side of the equation. -122 + 20x + 122 + x2 = 0 + 122 Reorder the terms: -122 + 122 + 20x + x2 = 0 + 122 Combine like terms: -122 + 122 = 0 0 + 20x + x2 = 0 + 122 20x + x2 = 0 + 122 Combine like terms: 0 + 122 = 122 20x + x2 = 122 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 122 + 100 Reorder the terms: 100 + 20x + x2 = 122 + 100 Combine like terms: 122 + 100 = 222 100 + 20x + x2 = 222 Factor a perfect square on the left side: (x + 10)(x + 10) = 222 Calculate the square root of the right side: 14.899664426 Break this problem into two subproblems by setting (x + 10) equal to 14.899664426 and -14.899664426.Subproblem 1
x + 10 = 14.899664426 Simplifying x + 10 = 14.899664426 Reorder the terms: 10 + x = 14.899664426 Solving 10 + x = 14.899664426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 14.899664426 + -10 Combine like terms: 10 + -10 = 0 0 + x = 14.899664426 + -10 x = 14.899664426 + -10 Combine like terms: 14.899664426 + -10 = 4.899664426 x = 4.899664426 Simplifying x = 4.899664426Subproblem 2
x + 10 = -14.899664426 Simplifying x + 10 = -14.899664426 Reorder the terms: 10 + x = -14.899664426 Solving 10 + x = -14.899664426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -14.899664426 + -10 Combine like terms: 10 + -10 = 0 0 + x = -14.899664426 + -10 x = -14.899664426 + -10 Combine like terms: -14.899664426 + -10 = -24.899664426 x = -24.899664426 Simplifying x = -24.899664426Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.899664426, -24.899664426}
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