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Simplifying 300 = 400x2 + -1x4 Solving 300 = 400x2 + -1x4 Solving for variable 'x'. Reorder the terms: 300 + -400x2 + x4 = 400x2 + -400x2 + -1x4 + x4 Combine like terms: 400x2 + -400x2 = 0 300 + -400x2 + x4 = 0 + -1x4 + x4 300 + -400x2 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 300 + -400x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-300' to each side of the equation. 300 + -400x2 + -300 + x4 = 0 + -300 Reorder the terms: 300 + -300 + -400x2 + x4 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -400x2 + x4 = 0 + -300 -400x2 + x4 = 0 + -300 Combine like terms: 0 + -300 = -300 -400x2 + x4 = -300 The x term is -400x2. Take half its coefficient (-200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. -400x2 + 40000 + x4 = -300 + 40000 Reorder the terms: 40000 + -400x2 + x4 = -300 + 40000 Combine like terms: -300 + 40000 = 39700 40000 + -400x2 + x4 = 39700 Factor a perfect square on the left side: (x2 + -200)(x2 + -200) = 39700 Calculate the square root of the right side: 199.248588452 Break this problem into two subproblems by setting (x2 + -200) equal to 199.248588452 and -199.248588452.Subproblem 1
x2 + -200 = 199.248588452 Simplifying x2 + -200 = 199.248588452 Reorder the terms: -200 + x2 = 199.248588452 Solving -200 + x2 = 199.248588452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x2 = 199.248588452 + 200 Combine like terms: -200 + 200 = 0 0 + x2 = 199.248588452 + 200 x2 = 199.248588452 + 200 Combine like terms: 199.248588452 + 200 = 399.248588452 x2 = 399.248588452 Simplifying x2 = 399.248588452 Take the square root of each side: x = {-19.981205881, 19.981205881}Subproblem 2
x2 + -200 = -199.248588452 Simplifying x2 + -200 = -199.248588452 Reorder the terms: -200 + x2 = -199.248588452 Solving -200 + x2 = -199.248588452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x2 = -199.248588452 + 200 Combine like terms: -200 + 200 = 0 0 + x2 = -199.248588452 + 200 x2 = -199.248588452 + 200 Combine like terms: -199.248588452 + 200 = 0.751411548 x2 = 0.751411548 Simplifying x2 = 0.751411548 Take the square root of each side: x = {-0.866839978, 0.866839978}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-19.981205881, 19.981205881, -0.866839978, 0.866839978}
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