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Simplifying x2 + -20x + -30 = 0 Reorder the terms: -30 + -20x + x2 = 0 Solving -30 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -20x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -20x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -20x + x2 = 0 + 30 -20x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -20x + x2 = 30 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 = 30 + 100 Reorder the terms: 100 + -20x + x2 = 30 + 100 Combine like terms: 30 + 100 = 130 100 + -20x + x2 = 130 Factor a perfect square on the left side: (x + -10)(x + -10) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (x + -10) equal to 11.401754251 and -11.401754251.Subproblem 1
x + -10 = 11.401754251 Simplifying x + -10 = 11.401754251 Reorder the terms: -10 + x = 11.401754251 Solving -10 + x = 11.401754251 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 = 11.401754251 + 10 Combine like terms: -10 + 10 = 0 0 + x = 11.401754251 + 10 x = 11.401754251 + 10 Combine like terms: 11.401754251 + 10 = 21.401754251 x = 21.401754251 Simplifying x = 21.401754251Subproblem 2
x + -10 = -11.401754251 Simplifying x + -10 = -11.401754251 Reorder the terms: -10 + x = -11.401754251 Solving -10 + x = -11.401754251 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 = -11.401754251 + 10 Combine like terms: -10 + 10 = 0 0 + x = -11.401754251 + 10 x = -11.401754251 + 10 Combine like terms: -11.401754251 + 10 = -1.401754251 x = -1.401754251 Simplifying x = -1.401754251Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.401754251, -1.401754251}
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