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Simplifying 2x2 + 20x + 20 = x2 Reorder the terms: 20 + 20x + 2x2 = x2 Solving 20 + 20x + 2x2 = x2 Solving for variable 'x'. Combine like terms: 2x2 + -1x2 = 1x2 20 + 20x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 20 + 20x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 20x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 20x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 20x + x2 = 0 + -20 20x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 20x + x2 = -20 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 = -20 + 100 Reorder the terms: 100 + 20x + x2 = -20 + 100 Combine like terms: -20 + 100 = 80 100 + 20x + x2 = 80 Factor a perfect square on the left side: (x + 10)(x + 10) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + 10) equal to 8.94427191 and -8.94427191.Subproblem 1
x + 10 = 8.94427191 Simplifying x + 10 = 8.94427191 Reorder the terms: 10 + x = 8.94427191 Solving 10 + x = 8.94427191 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 = 8.94427191 + -10 Combine like terms: 10 + -10 = 0 0 + x = 8.94427191 + -10 x = 8.94427191 + -10 Combine like terms: 8.94427191 + -10 = -1.05572809 x = -1.05572809 Simplifying x = -1.05572809Subproblem 2
x + 10 = -8.94427191 Simplifying x + 10 = -8.94427191 Reorder the terms: 10 + x = -8.94427191 Solving 10 + x = -8.94427191 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 = -8.94427191 + -10 Combine like terms: 10 + -10 = 0 0 + x = -8.94427191 + -10 x = -8.94427191 + -10 Combine like terms: -8.94427191 + -10 = -18.94427191 x = -18.94427191 Simplifying x = -18.94427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.05572809, -18.94427191}
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