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Simplifying 0.1x2 + 16x + -100 = 0 Reorder the terms: -100 + 16x + 0.1x2 = 0 Solving -100 + 16x + 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'. -1000 + 160x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 160x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 160x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 160x + x2 = 0 + 1000 160x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 160x + x2 = 1000 The x term is 160x. Take half its coefficient (80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. 160x + 6400 + x2 = 1000 + 6400 Reorder the terms: 6400 + 160x + x2 = 1000 + 6400 Combine like terms: 1000 + 6400 = 7400 6400 + 160x + x2 = 7400 Factor a perfect square on the left side: (x + 80)(x + 80) = 7400 Calculate the square root of the right side: 86.02325267 Break this problem into two subproblems by setting (x + 80) equal to 86.02325267 and -86.02325267.Subproblem 1
x + 80 = 86.02325267 Simplifying x + 80 = 86.02325267 Reorder the terms: 80 + x = 86.02325267 Solving 80 + x = 86.02325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = 86.02325267 + -80 Combine like terms: 80 + -80 = 0 0 + x = 86.02325267 + -80 x = 86.02325267 + -80 Combine like terms: 86.02325267 + -80 = 6.02325267 x = 6.02325267 Simplifying x = 6.02325267Subproblem 2
x + 80 = -86.02325267 Simplifying x + 80 = -86.02325267 Reorder the terms: 80 + x = -86.02325267 Solving 80 + x = -86.02325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + -80 + x = -86.02325267 + -80 Combine like terms: 80 + -80 = 0 0 + x = -86.02325267 + -80 x = -86.02325267 + -80 Combine like terms: -86.02325267 + -80 = -166.02325267 x = -166.02325267 Simplifying x = -166.02325267Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.02325267, -166.02325267}
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