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Simplifying 0.25x2 + -60x + 3600 = 0 Reorder the terms: 3600 + -60x + 0.25x2 = 0 Solving 3600 + -60x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 14400 + -240x + x2 = 0 Move the constant term to the right: Add '-14400' to each side of the equation. 14400 + -240x + -14400 + x2 = 0 + -14400 Reorder the terms: 14400 + -14400 + -240x + x2 = 0 + -14400 Combine like terms: 14400 + -14400 = 0 0 + -240x + x2 = 0 + -14400 -240x + x2 = 0 + -14400 Combine like terms: 0 + -14400 = -14400 -240x + x2 = -14400 The x term is -240x. Take half its coefficient (-120). Square it (14400) and add it to both sides. Add '14400' to each side of the equation. -240x + 14400 + x2 = -14400 + 14400 Reorder the terms: 14400 + -240x + x2 = -14400 + 14400 Combine like terms: -14400 + 14400 = 0 14400 + -240x + x2 = 0 Factor a perfect square on the left side: (x + -120)(x + -120) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -120) equal to 0 and 0.Subproblem 1
x + -120 = 0 Simplifying x + -120 = 0 Reorder the terms: -120 + x = 0 Solving -120 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + x = 0 + 120 Combine like terms: -120 + 120 = 0 0 + x = 0 + 120 x = 0 + 120 Combine like terms: 0 + 120 = 120 x = 120 Simplifying x = 120Subproblem 2
x + -120 = 0 Simplifying x + -120 = 0 Reorder the terms: -120 + x = 0 Solving -120 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '120' to each side of the equation. -120 + 120 + x = 0 + 120 Combine like terms: -120 + 120 = 0 0 + x = 0 + 120 x = 0 + 120 Combine like terms: 0 + 120 = 120 x = 120 Simplifying x = 120Solution
The solution to the problem is based on the solutions from the subproblems. x = {120, 120}
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