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Simplifying 2x2 + 80x + 400 = 0 Reorder the terms: 400 + 80x + 2x2 = 0 Solving 400 + 80x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(200 + 40x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(200 + 40x + x2)' equal to zero and attempt to solve: Simplifying 200 + 40x + x2 = 0 Solving 200 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + 40x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + 40x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + 40x + x2 = 0 + -200 40x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 40x + x2 = -200 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 = -200 + 400 Reorder the terms: 400 + 40x + x2 = -200 + 400 Combine like terms: -200 + 400 = 200 400 + 40x + x2 = 200 Factor a perfect square on the left side: (x + 20)(x + 20) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + 20) equal to 14.142135624 and -14.142135624.Subproblem 1
x + 20 = 14.142135624 Simplifying x + 20 = 14.142135624 Reorder the terms: 20 + x = 14.142135624 Solving 20 + x = 14.142135624 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 = 14.142135624 + -20 Combine like terms: 20 + -20 = 0 0 + x = 14.142135624 + -20 x = 14.142135624 + -20 Combine like terms: 14.142135624 + -20 = -5.857864376 x = -5.857864376 Simplifying x = -5.857864376Subproblem 2
x + 20 = -14.142135624 Simplifying x + 20 = -14.142135624 Reorder the terms: 20 + x = -14.142135624 Solving 20 + x = -14.142135624 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 = -14.142135624 + -20 Combine like terms: 20 + -20 = 0 0 + x = -14.142135624 + -20 x = -14.142135624 + -20 Combine like terms: -14.142135624 + -20 = -34.142135624 x = -34.142135624 Simplifying x = -34.142135624Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.857864376, -34.142135624}Solution
x = {-5.857864376, -34.142135624}
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