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Simplifying 0.01x2 + 0.1x + -97.76 = 0 Reorder the terms: -97.76 + 0.1x + 0.01x2 = 0 Solving -97.76 + 0.1x + 0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -9776 + 10x + x2 = 0 Move the constant term to the right: Add '9776' to each side of the equation. -9776 + 10x + 9776 + x2 = 0 + 9776 Reorder the terms: -9776 + 9776 + 10x + x2 = 0 + 9776 Combine like terms: -9776 + 9776 = 0 0 + 10x + x2 = 0 + 9776 10x + x2 = 0 + 9776 Combine like terms: 0 + 9776 = 9776 10x + x2 = 9776 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 9776 + 25 Reorder the terms: 25 + 10x + x2 = 9776 + 25 Combine like terms: 9776 + 25 = 9801 25 + 10x + x2 = 9801 Factor a perfect square on the left side: (x + 5)(x + 5) = 9801 Calculate the square root of the right side: 99 Break this problem into two subproblems by setting (x + 5) equal to 99 and -99.Subproblem 1
x + 5 = 99 Simplifying x + 5 = 99 Reorder the terms: 5 + x = 99 Solving 5 + x = 99 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 99 + -5 Combine like terms: 5 + -5 = 0 0 + x = 99 + -5 x = 99 + -5 Combine like terms: 99 + -5 = 94 x = 94 Simplifying x = 94Subproblem 2
x + 5 = -99 Simplifying x + 5 = -99 Reorder the terms: 5 + x = -99 Solving 5 + x = -99 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -99 + -5 Combine like terms: 5 + -5 = 0 0 + x = -99 + -5 x = -99 + -5 Combine like terms: -99 + -5 = -104 x = -104 Simplifying x = -104Solution
The solution to the problem is based on the solutions from the subproblems. x = {94, -104}
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