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Simplifying x2 = 400 + -10x Solving x2 = 400 + -10x Solving for variable 'x'. Reorder the terms: -400 + 10x + x2 = 400 + -10x + -400 + 10x Reorder the terms: -400 + 10x + x2 = 400 + -400 + -10x + 10x Combine like terms: 400 + -400 = 0 -400 + 10x + x2 = 0 + -10x + 10x -400 + 10x + x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -400 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 10x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 10x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 10x + x2 = 0 + 400 10x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 10x + x2 = 400 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 400 + 25 Reorder the terms: 25 + 10x + x2 = 400 + 25 Combine like terms: 400 + 25 = 425 25 + 10x + x2 = 425 Factor a perfect square on the left side: (x + 5)(x + 5) = 425 Calculate the square root of the right side: 20.615528128 Break this problem into two subproblems by setting (x + 5) equal to 20.615528128 and -20.615528128.Subproblem 1
x + 5 = 20.615528128 Simplifying x + 5 = 20.615528128 Reorder the terms: 5 + x = 20.615528128 Solving 5 + x = 20.615528128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 20.615528128 + -5 Combine like terms: 5 + -5 = 0 0 + x = 20.615528128 + -5 x = 20.615528128 + -5 Combine like terms: 20.615528128 + -5 = 15.615528128 x = 15.615528128 Simplifying x = 15.615528128Subproblem 2
x + 5 = -20.615528128 Simplifying x + 5 = -20.615528128 Reorder the terms: 5 + x = -20.615528128 Solving 5 + x = -20.615528128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -20.615528128 + -5 Combine like terms: 5 + -5 = 0 0 + x = -20.615528128 + -5 x = -20.615528128 + -5 Combine like terms: -20.615528128 + -5 = -25.615528128 x = -25.615528128 Simplifying x = -25.615528128Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.615528128, -25.615528128}
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