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Simplifying 0 = 10x2 + -400x + -409 Reorder the terms: 0 = -409 + -400x + 10x2 Solving 0 = -409 + -400x + 10x2 Solving for variable 'x'. Combine like terms: 0 + 409 = 409 409 + 400x + -10x2 = -409 + -400x + 10x2 + 409 + 400x + -10x2 Reorder the terms: 409 + 400x + -10x2 = -409 + 409 + -400x + 400x + 10x2 + -10x2 Combine like terms: -409 + 409 = 0 409 + 400x + -10x2 = 0 + -400x + 400x + 10x2 + -10x2 409 + 400x + -10x2 = -400x + 400x + 10x2 + -10x2 Combine like terms: -400x + 400x = 0 409 + 400x + -10x2 = 0 + 10x2 + -10x2 409 + 400x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 409 + 400x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -40.9 + -40x + x2 = 0 Move the constant term to the right: Add '40.9' to each side of the equation. -40.9 + -40x + 40.9 + x2 = 0 + 40.9 Reorder the terms: -40.9 + 40.9 + -40x + x2 = 0 + 40.9 Combine like terms: -40.9 + 40.9 = 0.0 0.0 + -40x + x2 = 0 + 40.9 -40x + x2 = 0 + 40.9 Combine like terms: 0 + 40.9 = 40.9 -40x + x2 = 40.9 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 = 40.9 + 400 Reorder the terms: 400 + -40x + x2 = 40.9 + 400 Combine like terms: 40.9 + 400 = 440.9 400 + -40x + x2 = 440.9 Factor a perfect square on the left side: (x + -20)(x + -20) = 440.9 Calculate the square root of the right side: 20.997618913 Break this problem into two subproblems by setting (x + -20) equal to 20.997618913 and -20.997618913.Subproblem 1
x + -20 = 20.997618913 Simplifying x + -20 = 20.997618913 Reorder the terms: -20 + x = 20.997618913 Solving -20 + x = 20.997618913 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 = 20.997618913 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.997618913 + 20 x = 20.997618913 + 20 Combine like terms: 20.997618913 + 20 = 40.997618913 x = 40.997618913 Simplifying x = 40.997618913Subproblem 2
x + -20 = -20.997618913 Simplifying x + -20 = -20.997618913 Reorder the terms: -20 + x = -20.997618913 Solving -20 + x = -20.997618913 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 = -20.997618913 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.997618913 + 20 x = -20.997618913 + 20 Combine like terms: -20.997618913 + 20 = -0.997618913 x = -0.997618913 Simplifying x = -0.997618913Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.997618913, -0.997618913}
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