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Simplifying 80 + 6X + 0.1X2 = 0 Solving 80 + 6X + 0.1X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 800 + 60X + X2 = 0 Move the constant term to the right: Add '-800' to each side of the equation. 800 + 60X + -800 + X2 = 0 + -800 Reorder the terms: 800 + -800 + 60X + X2 = 0 + -800 Combine like terms: 800 + -800 = 0 0 + 60X + X2 = 0 + -800 60X + X2 = 0 + -800 Combine like terms: 0 + -800 = -800 60X + X2 = -800 The X term is 60X. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60X + 900 + X2 = -800 + 900 Reorder the terms: 900 + 60X + X2 = -800 + 900 Combine like terms: -800 + 900 = 100 900 + 60X + X2 = 100 Factor a perfect square on the left side: (X + 30)(X + 30) = 100 Calculate the square root of the right side: 10 Break this problem into two subproblems by setting (X + 30) equal to 10 and -10.Subproblem 1
X + 30 = 10 Simplifying X + 30 = 10 Reorder the terms: 30 + X = 10 Solving 30 + X = 10 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + X = 10 + -30 Combine like terms: 30 + -30 = 0 0 + X = 10 + -30 X = 10 + -30 Combine like terms: 10 + -30 = -20 X = -20 Simplifying X = -20Subproblem 2
X + 30 = -10 Simplifying X + 30 = -10 Reorder the terms: 30 + X = -10 Solving 30 + X = -10 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + X = -10 + -30 Combine like terms: 30 + -30 = 0 0 + X = -10 + -30 X = -10 + -30 Combine like terms: -10 + -30 = -40 X = -40 Simplifying X = -40Solution
The solution to the problem is based on the solutions from the subproblems. X = {-20, -40}
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