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Simplifying 0.01x2 + -13x + 3600 = 0 Reorder the terms: 3600 + -13x + 0.01x2 = 0 Solving 3600 + -13x + 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'. 360000 + -1300x + x2 = 0 Move the constant term to the right: Add '-360000' to each side of the equation. 360000 + -1300x + -360000 + x2 = 0 + -360000 Reorder the terms: 360000 + -360000 + -1300x + x2 = 0 + -360000 Combine like terms: 360000 + -360000 = 0 0 + -1300x + x2 = 0 + -360000 -1300x + x2 = 0 + -360000 Combine like terms: 0 + -360000 = -360000 -1300x + x2 = -360000 The x term is -1300x. Take half its coefficient (-650). Square it (422500) and add it to both sides. Add '422500' to each side of the equation. -1300x + 422500 + x2 = -360000 + 422500 Reorder the terms: 422500 + -1300x + x2 = -360000 + 422500 Combine like terms: -360000 + 422500 = 62500 422500 + -1300x + x2 = 62500 Factor a perfect square on the left side: (x + -650)(x + -650) = 62500 Calculate the square root of the right side: 250 Break this problem into two subproblems by setting (x + -650) equal to 250 and -250.Subproblem 1
x + -650 = 250 Simplifying x + -650 = 250 Reorder the terms: -650 + x = 250 Solving -650 + x = 250 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '650' to each side of the equation. -650 + 650 + x = 250 + 650 Combine like terms: -650 + 650 = 0 0 + x = 250 + 650 x = 250 + 650 Combine like terms: 250 + 650 = 900 x = 900 Simplifying x = 900Subproblem 2
x + -650 = -250 Simplifying x + -650 = -250 Reorder the terms: -650 + x = -250 Solving -650 + x = -250 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '650' to each side of the equation. -650 + 650 + x = -250 + 650 Combine like terms: -650 + 650 = 0 0 + x = -250 + 650 x = -250 + 650 Combine like terms: -250 + 650 = 400 x = 400 Simplifying x = 400Solution
The solution to the problem is based on the solutions from the subproblems. x = {900, 400}
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