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Simplifying 576 = 10x + -0.04x2 Solving 576 = 10x + -0.04x2 Solving for variable 'x'. Reorder the terms: 576 + -10x + 0.04x2 = 10x + -10x + -0.04x2 + 0.04x2 Combine like terms: 10x + -10x = 0 576 + -10x + 0.04x2 = 0 + -0.04x2 + 0.04x2 576 + -10x + 0.04x2 = -0.04x2 + 0.04x2 Combine like terms: -0.04x2 + 0.04x2 = 0.00 576 + -10x + 0.04x2 = 0.00 Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 14400 + -250x + x2 = 0 Move the constant term to the right: Add '-14400' to each side of the equation. 14400 + -250x + -14400 + x2 = 0 + -14400 Reorder the terms: 14400 + -14400 + -250x + x2 = 0 + -14400 Combine like terms: 14400 + -14400 = 0 0 + -250x + x2 = 0 + -14400 -250x + x2 = 0 + -14400 Combine like terms: 0 + -14400 = -14400 -250x + x2 = -14400 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 = -14400 + 15625 Reorder the terms: 15625 + -250x + x2 = -14400 + 15625 Combine like terms: -14400 + 15625 = 1225 15625 + -250x + x2 = 1225 Factor a perfect square on the left side: (x + -125)(x + -125) = 1225 Calculate the square root of the right side: 35 Break this problem into two subproblems by setting (x + -125) equal to 35 and -35.Subproblem 1
x + -125 = 35 Simplifying x + -125 = 35 Reorder the terms: -125 + x = 35 Solving -125 + x = 35 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 = 35 + 125 Combine like terms: -125 + 125 = 0 0 + x = 35 + 125 x = 35 + 125 Combine like terms: 35 + 125 = 160 x = 160 Simplifying x = 160Subproblem 2
x + -125 = -35 Simplifying x + -125 = -35 Reorder the terms: -125 + x = -35 Solving -125 + x = -35 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 = -35 + 125 Combine like terms: -125 + 125 = 0 0 + x = -35 + 125 x = -35 + 125 Combine like terms: -35 + 125 = 90 x = 90 Simplifying x = 90Solution
The solution to the problem is based on the solutions from the subproblems. x = {160, 90}
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