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Simplifying 0.1x2 + -13x + 360 = 0 Reorder the terms: 360 + -13x + 0.1x2 = 0 Solving 360 + -13x + 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'. 3600 + -130x + x2 = 0 Move the constant term to the right: Add '-3600' to each side of the equation. 3600 + -130x + -3600 + x2 = 0 + -3600 Reorder the terms: 3600 + -3600 + -130x + x2 = 0 + -3600 Combine like terms: 3600 + -3600 = 0 0 + -130x + x2 = 0 + -3600 -130x + x2 = 0 + -3600 Combine like terms: 0 + -3600 = -3600 -130x + x2 = -3600 The x term is -130x. Take half its coefficient (-65). Square it (4225) and add it to both sides. Add '4225' to each side of the equation. -130x + 4225 + x2 = -3600 + 4225 Reorder the terms: 4225 + -130x + x2 = -3600 + 4225 Combine like terms: -3600 + 4225 = 625 4225 + -130x + x2 = 625 Factor a perfect square on the left side: (x + -65)(x + -65) = 625 Calculate the square root of the right side: 25 Break this problem into two subproblems by setting (x + -65) equal to 25 and -25.Subproblem 1
x + -65 = 25 Simplifying x + -65 = 25 Reorder the terms: -65 + x = 25 Solving -65 + x = 25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = 25 + 65 Combine like terms: -65 + 65 = 0 0 + x = 25 + 65 x = 25 + 65 Combine like terms: 25 + 65 = 90 x = 90 Simplifying x = 90Subproblem 2
x + -65 = -25 Simplifying x + -65 = -25 Reorder the terms: -65 + x = -25 Solving -65 + x = -25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = -25 + 65 Combine like terms: -65 + 65 = 0 0 + x = -25 + 65 x = -25 + 65 Combine like terms: -25 + 65 = 40 x = 40 Simplifying x = 40Solution
The solution to the problem is based on the solutions from the subproblems. x = {90, 40}
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