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Simplifying 100 = 0.5x(x + 10) Reorder the terms: 100 = 0.5x(10 + x) 100 = (10 * 0.5x + x * 0.5x) 100 = (5x + 0.5x2) Solving 100 = 5x + 0.5x2 Solving for variable 'x'. Reorder the terms: 100 + -5x + -0.5x2 = 5x + -5x + 0.5x2 + -0.5x2 Combine like terms: 5x + -5x = 0 100 + -5x + -0.5x2 = 0 + 0.5x2 + -0.5x2 100 + -5x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 100 + -5x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -200 + 10x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 10x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 10x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 10x + x2 = 0 + 200 10x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 10x + x2 = 200 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 = 200 + 25 Reorder the terms: 25 + 10x + x2 = 200 + 25 Combine like terms: 200 + 25 = 225 25 + 10x + x2 = 225 Factor a perfect square on the left side: (x + 5)(x + 5) = 225 Calculate the square root of the right side: 15 Break this problem into two subproblems by setting (x + 5) equal to 15 and -15.Subproblem 1
x + 5 = 15 Simplifying x + 5 = 15 Reorder the terms: 5 + x = 15 Solving 5 + x = 15 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 = 15 + -5 Combine like terms: 5 + -5 = 0 0 + x = 15 + -5 x = 15 + -5 Combine like terms: 15 + -5 = 10 x = 10 Simplifying x = 10Subproblem 2
x + 5 = -15 Simplifying x + 5 = -15 Reorder the terms: 5 + x = -15 Solving 5 + x = -15 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 = -15 + -5 Combine like terms: 5 + -5 = 0 0 + x = -15 + -5 x = -15 + -5 Combine like terms: -15 + -5 = -20 x = -20 Simplifying x = -20Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -20}
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