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Simplifying 10x + -0.04x2 = 400 Solving 10x + -0.04x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + 10x + -0.04x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + 10x + -0.04x2 = 0 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. 10000 + -250x + x2 = 0 Move the constant term to the right: Add '-10000' to each side of the equation. 10000 + -250x + -10000 + x2 = 0 + -10000 Reorder the terms: 10000 + -10000 + -250x + x2 = 0 + -10000 Combine like terms: 10000 + -10000 = 0 0 + -250x + x2 = 0 + -10000 -250x + x2 = 0 + -10000 Combine like terms: 0 + -10000 = -10000 -250x + x2 = -10000 The x term is -250x. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250x + 15625 + x2 = -10000 + 15625 Reorder the terms: 15625 + -250x + x2 = -10000 + 15625 Combine like terms: -10000 + 15625 = 5625 15625 + -250x + x2 = 5625 Factor a perfect square on the left side: (x + -125)(x + -125) = 5625 Calculate the square root of the right side: 75 Break this problem into two subproblems by setting (x + -125) equal to 75 and -75.Subproblem 1
x + -125 = 75 Simplifying x + -125 = 75 Reorder the terms: -125 + x = 75 Solving -125 + x = 75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 75 + 125 Combine like terms: -125 + 125 = 0 0 + x = 75 + 125 x = 75 + 125 Combine like terms: 75 + 125 = 200 x = 200 Simplifying x = 200Subproblem 2
x + -125 = -75 Simplifying x + -125 = -75 Reorder the terms: -125 + x = -75 Solving -125 + x = -75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -75 + 125 Combine like terms: -125 + 125 = 0 0 + x = -75 + 125 x = -75 + 125 Combine like terms: -75 + 125 = 50 x = 50 Simplifying x = 50Solution
The solution to the problem is based on the solutions from the subproblems. x = {200, 50}
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