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Simplifying x2 + -20x + -600 = 0 Reorder the terms: -600 + -20x + x2 = 0 Solving -600 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + -20x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + -20x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -20x + x2 = 0 + 600 -20x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 -20x + x2 = 600 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 = 600 + 100 Reorder the terms: 100 + -20x + x2 = 600 + 100 Combine like terms: 600 + 100 = 700 100 + -20x + x2 = 700 Factor a perfect square on the left side: (x + -10)(x + -10) = 700 Calculate the square root of the right side: 26.457513111 Break this problem into two subproblems by setting (x + -10) equal to 26.457513111 and -26.457513111.Subproblem 1
x + -10 = 26.457513111 Simplifying x + -10 = 26.457513111 Reorder the terms: -10 + x = 26.457513111 Solving -10 + x = 26.457513111 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 = 26.457513111 + 10 Combine like terms: -10 + 10 = 0 0 + x = 26.457513111 + 10 x = 26.457513111 + 10 Combine like terms: 26.457513111 + 10 = 36.457513111 x = 36.457513111 Simplifying x = 36.457513111Subproblem 2
x + -10 = -26.457513111 Simplifying x + -10 = -26.457513111 Reorder the terms: -10 + x = -26.457513111 Solving -10 + x = -26.457513111 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 = -26.457513111 + 10 Combine like terms: -10 + 10 = 0 0 + x = -26.457513111 + 10 x = -26.457513111 + 10 Combine like terms: -26.457513111 + 10 = -16.457513111 x = -16.457513111 Simplifying x = -16.457513111Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.457513111, -16.457513111}
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