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Simplifying (x + 20)(x + 20) = 14 Reorder the terms: (20 + x)(x + 20) = 14 Reorder the terms: (20 + x)(20 + x) = 14 Multiply (20 + x) * (20 + x) (20(20 + x) + x(20 + x)) = 14 ((20 * 20 + x * 20) + x(20 + x)) = 14 ((400 + 20x) + x(20 + x)) = 14 (400 + 20x + (20 * x + x * x)) = 14 (400 + 20x + (20x + x2)) = 14 Combine like terms: 20x + 20x = 40x (400 + 40x + x2) = 14 Solving 400 + 40x + x2 = 14 Solving for variable 'x'. Reorder the terms: 400 + -14 + 40x + x2 = 14 + -14 Combine like terms: 400 + -14 = 386 386 + 40x + x2 = 14 + -14 Combine like terms: 14 + -14 = 0 386 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-386' to each side of the equation. 386 + 40x + -386 + x2 = 0 + -386 Reorder the terms: 386 + -386 + 40x + x2 = 0 + -386 Combine like terms: 386 + -386 = 0 0 + 40x + x2 = 0 + -386 40x + x2 = 0 + -386 Combine like terms: 0 + -386 = -386 40x + x2 = -386 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = -386 + 400 Reorder the terms: 400 + 40x + x2 = -386 + 400 Combine like terms: -386 + 400 = 14 400 + 40x + x2 = 14 Factor a perfect square on the left side: (x + 20)(x + 20) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 20) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 20 = 3.741657387 Simplifying x + 20 = 3.741657387 Reorder the terms: 20 + x = 3.741657387 Solving 20 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 3.741657387 + -20 Combine like terms: 20 + -20 = 0 0 + x = 3.741657387 + -20 x = 3.741657387 + -20 Combine like terms: 3.741657387 + -20 = -16.258342613 x = -16.258342613 Simplifying x = -16.258342613Subproblem 2
x + 20 = -3.741657387 Simplifying x + 20 = -3.741657387 Reorder the terms: 20 + x = -3.741657387 Solving 20 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -3.741657387 + -20 Combine like terms: 20 + -20 = 0 0 + x = -3.741657387 + -20 x = -3.741657387 + -20 Combine like terms: -3.741657387 + -20 = -23.741657387 x = -23.741657387 Simplifying x = -23.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {-16.258342613, -23.741657387}
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