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Simplifying -10x + 0.25x2 = 1600 Solving -10x + 0.25x2 = 1600 Solving for variable 'x'. Reorder the terms: -1600 + -10x + 0.25x2 = 1600 + -1600 Combine like terms: 1600 + -1600 = 0 -1600 + -10x + 0.25x2 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -6400 + -40x + x2 = 0 Move the constant term to the right: Add '6400' to each side of the equation. -6400 + -40x + 6400 + x2 = 0 + 6400 Reorder the terms: -6400 + 6400 + -40x + x2 = 0 + 6400 Combine like terms: -6400 + 6400 = 0 0 + -40x + x2 = 0 + 6400 -40x + x2 = 0 + 6400 Combine like terms: 0 + 6400 = 6400 -40x + x2 = 6400 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 6400 + 400 Reorder the terms: 400 + -40x + x2 = 6400 + 400 Combine like terms: 6400 + 400 = 6800 400 + -40x + x2 = 6800 Factor a perfect square on the left side: (x + -20)(x + -20) = 6800 Calculate the square root of the right side: 82.462112512 Break this problem into two subproblems by setting (x + -20) equal to 82.462112512 and -82.462112512.Subproblem 1
x + -20 = 82.462112512 Simplifying x + -20 = 82.462112512 Reorder the terms: -20 + x = 82.462112512 Solving -20 + x = 82.462112512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 82.462112512 + 20 Combine like terms: -20 + 20 = 0 0 + x = 82.462112512 + 20 x = 82.462112512 + 20 Combine like terms: 82.462112512 + 20 = 102.462112512 x = 102.462112512 Simplifying x = 102.462112512Subproblem 2
x + -20 = -82.462112512 Simplifying x + -20 = -82.462112512 Reorder the terms: -20 + x = -82.462112512 Solving -20 + x = -82.462112512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -82.462112512 + 20 Combine like terms: -20 + 20 = 0 0 + x = -82.462112512 + 20 x = -82.462112512 + 20 Combine like terms: -82.462112512 + 20 = -62.462112512 x = -62.462112512 Simplifying x = -62.462112512Solution
The solution to the problem is based on the solutions from the subproblems. x = {102.462112512, -62.462112512}
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