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Simplifying -0.01x2 + -0.10x + 101.76 = 0 Reorder the terms: 101.76 + -0.10x + -0.01x2 = 0 Solving 101.76 + -0.10x + -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'. -10176 + 10x + x2 = 0 Move the constant term to the right: Add '10176' to each side of the equation. -10176 + 10x + 10176 + x2 = 0 + 10176 Reorder the terms: -10176 + 10176 + 10x + x2 = 0 + 10176 Combine like terms: -10176 + 10176 = 0 0 + 10x + x2 = 0 + 10176 10x + x2 = 0 + 10176 Combine like terms: 0 + 10176 = 10176 10x + x2 = 10176 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 = 10176 + 25 Reorder the terms: 25 + 10x + x2 = 10176 + 25 Combine like terms: 10176 + 25 = 10201 25 + 10x + x2 = 10201 Factor a perfect square on the left side: (x + 5)(x + 5) = 10201 Calculate the square root of the right side: 101 Break this problem into two subproblems by setting (x + 5) equal to 101 and -101.Subproblem 1
x + 5 = 101 Simplifying x + 5 = 101 Reorder the terms: 5 + x = 101 Solving 5 + x = 101 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 = 101 + -5 Combine like terms: 5 + -5 = 0 0 + x = 101 + -5 x = 101 + -5 Combine like terms: 101 + -5 = 96 x = 96 Simplifying x = 96Subproblem 2
x + 5 = -101 Simplifying x + 5 = -101 Reorder the terms: 5 + x = -101 Solving 5 + x = -101 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 = -101 + -5 Combine like terms: 5 + -5 = 0 0 + x = -101 + -5 x = -101 + -5 Combine like terms: -101 + -5 = -106 x = -106 Simplifying x = -106Solution
The solution to the problem is based on the solutions from the subproblems. x = {96, -106}
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