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Simplifying x2 + -20x = 50 Reorder the terms: -20x + x2 = 50 Solving -20x + x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + -20x + x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -20x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -20x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -20x + x2 = 0 + 50 -20x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -20x + x2 = 50 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 50 + 100 Reorder the terms: 100 + -20x + x2 = 50 + 100 Combine like terms: 50 + 100 = 150 100 + -20x + x2 = 150 Factor a perfect square on the left side: (x + -10)(x + -10) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (x + -10) equal to 12.247448714 and -12.247448714.Subproblem 1
x + -10 = 12.247448714 Simplifying x + -10 = 12.247448714 Reorder the terms: -10 + x = 12.247448714 Solving -10 + x = 12.247448714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 12.247448714 + 10 Combine like terms: -10 + 10 = 0 0 + x = 12.247448714 + 10 x = 12.247448714 + 10 Combine like terms: 12.247448714 + 10 = 22.247448714 x = 22.247448714 Simplifying x = 22.247448714Subproblem 2
x + -10 = -12.247448714 Simplifying x + -10 = -12.247448714 Reorder the terms: -10 + x = -12.247448714 Solving -10 + x = -12.247448714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -12.247448714 + 10 Combine like terms: -10 + 10 = 0 0 + x = -12.247448714 + 10 x = -12.247448714 + 10 Combine like terms: -12.247448714 + 10 = -2.247448714 x = -2.247448714 Simplifying x = -2.247448714Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.247448714, -2.247448714}
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