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Simplifying 0 = x2 + -20x + 80 Reorder the terms: 0 = 80 + -20x + x2 Solving 0 = 80 + -20x + x2 Solving for variable 'x'. Combine like terms: 0 + -80 = -80 -80 + 20x + -1x2 = 80 + -20x + x2 + -80 + 20x + -1x2 Reorder the terms: -80 + 20x + -1x2 = 80 + -80 + -20x + 20x + x2 + -1x2 Combine like terms: 80 + -80 = 0 -80 + 20x + -1x2 = 0 + -20x + 20x + x2 + -1x2 -80 + 20x + -1x2 = -20x + 20x + x2 + -1x2 Combine like terms: -20x + 20x = 0 -80 + 20x + -1x2 = 0 + x2 + -1x2 -80 + 20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -80 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 80 + -20x + x2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -20x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -20x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -20x + x2 = 0 + -80 -20x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -20x + x2 = -80 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 = -80 + 100 Reorder the terms: 100 + -20x + x2 = -80 + 100 Combine like terms: -80 + 100 = 20 100 + -20x + x2 = 20 Factor a perfect square on the left side: (x + -10)(x + -10) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -10) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -10 = 4.472135955 Simplifying x + -10 = 4.472135955 Reorder the terms: -10 + x = 4.472135955 Solving -10 + x = 4.472135955 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 = 4.472135955 + 10 Combine like terms: -10 + 10 = 0 0 + x = 4.472135955 + 10 x = 4.472135955 + 10 Combine like terms: 4.472135955 + 10 = 14.472135955 x = 14.472135955 Simplifying x = 14.472135955Subproblem 2
x + -10 = -4.472135955 Simplifying x + -10 = -4.472135955 Reorder the terms: -10 + x = -4.472135955 Solving -10 + x = -4.472135955 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 = -4.472135955 + 10 Combine like terms: -10 + 10 = 0 0 + x = -4.472135955 + 10 x = -4.472135955 + 10 Combine like terms: -4.472135955 + 10 = 5.527864045 x = 5.527864045 Simplifying x = 5.527864045Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.472135955, 5.527864045}
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