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Simplifying 300 = 200x2 + -1x4 Solving 300 = 200x2 + -1x4 Solving for variable 'x'. Reorder the terms: 300 + -200x2 + x4 = 200x2 + -200x2 + -1x4 + x4 Combine like terms: 200x2 + -200x2 = 0 300 + -200x2 + x4 = 0 + -1x4 + x4 300 + -200x2 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 300 + -200x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-300' to each side of the equation. 300 + -200x2 + -300 + x4 = 0 + -300 Reorder the terms: 300 + -300 + -200x2 + x4 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -200x2 + x4 = 0 + -300 -200x2 + x4 = 0 + -300 Combine like terms: 0 + -300 = -300 -200x2 + x4 = -300 The x term is -200x2. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x2 + 10000 + x4 = -300 + 10000 Reorder the terms: 10000 + -200x2 + x4 = -300 + 10000 Combine like terms: -300 + 10000 = 9700 10000 + -200x2 + x4 = 9700 Factor a perfect square on the left side: (x2 + -100)(x2 + -100) = 9700 Calculate the square root of the right side: 98.488578018 Break this problem into two subproblems by setting (x2 + -100) equal to 98.488578018 and -98.488578018.Subproblem 1
x2 + -100 = 98.488578018 Simplifying x2 + -100 = 98.488578018 Reorder the terms: -100 + x2 = 98.488578018 Solving -100 + x2 = 98.488578018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x2 = 98.488578018 + 100 Combine like terms: -100 + 100 = 0 0 + x2 = 98.488578018 + 100 x2 = 98.488578018 + 100 Combine like terms: 98.488578018 + 100 = 198.488578018 x2 = 198.488578018 Simplifying x2 = 198.488578018 Take the square root of each side: x = {-14.088597447, 14.088597447}Subproblem 2
x2 + -100 = -98.488578018 Simplifying x2 + -100 = -98.488578018 Reorder the terms: -100 + x2 = -98.488578018 Solving -100 + x2 = -98.488578018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x2 = -98.488578018 + 100 Combine like terms: -100 + 100 = 0 0 + x2 = -98.488578018 + 100 x2 = -98.488578018 + 100 Combine like terms: -98.488578018 + 100 = 1.511421982 x2 = 1.511421982 Simplifying x2 = 1.511421982 Take the square root of each side: x = {-1.229399033, 1.229399033}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-14.088597447, 14.088597447, -1.229399033, 1.229399033}
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