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Simplifying 0.1x2 + -10x + -560 = 0 Reorder the terms: -560 + -10x + 0.1x2 = 0 Solving -560 + -10x + 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'. -5600 + -100x + x2 = 0 Move the constant term to the right: Add '5600' to each side of the equation. -5600 + -100x + 5600 + x2 = 0 + 5600 Reorder the terms: -5600 + 5600 + -100x + x2 = 0 + 5600 Combine like terms: -5600 + 5600 = 0 0 + -100x + x2 = 0 + 5600 -100x + x2 = 0 + 5600 Combine like terms: 0 + 5600 = 5600 -100x + x2 = 5600 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = 5600 + 2500 Reorder the terms: 2500 + -100x + x2 = 5600 + 2500 Combine like terms: 5600 + 2500 = 8100 2500 + -100x + x2 = 8100 Factor a perfect square on the left side: (x + -50)(x + -50) = 8100 Calculate the square root of the right side: 90 Break this problem into two subproblems by setting (x + -50) equal to 90 and -90.Subproblem 1
x + -50 = 90 Simplifying x + -50 = 90 Reorder the terms: -50 + x = 90 Solving -50 + x = 90 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 90 + 50 Combine like terms: -50 + 50 = 0 0 + x = 90 + 50 x = 90 + 50 Combine like terms: 90 + 50 = 140 x = 140 Simplifying x = 140Subproblem 2
x + -50 = -90 Simplifying x + -50 = -90 Reorder the terms: -50 + x = -90 Solving -50 + x = -90 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -90 + 50 Combine like terms: -50 + 50 = 0 0 + x = -90 + 50 x = -90 + 50 Combine like terms: -90 + 50 = -40 x = -40 Simplifying x = -40Solution
The solution to the problem is based on the solutions from the subproblems. x = {140, -40}
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