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Simplifying 0 = 2.4x2 + -24x + 60 Reorder the terms: 0 = 60 + -24x + 2.4x2 Solving 0 = 60 + -24x + 2.4x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + 24x + -2.4x2 = 60 + -24x + 2.4x2 + -60 + 24x + -2.4x2 Reorder the terms: -60 + 24x + -2.4x2 = 60 + -60 + -24x + 24x + 2.4x2 + -2.4x2 Combine like terms: 60 + -60 = 0 -60 + 24x + -2.4x2 = 0 + -24x + 24x + 2.4x2 + -2.4x2 -60 + 24x + -2.4x2 = -24x + 24x + 2.4x2 + -2.4x2 Combine like terms: -24x + 24x = 0 -60 + 24x + -2.4x2 = 0 + 2.4x2 + -2.4x2 -60 + 24x + -2.4x2 = 2.4x2 + -2.4x2 Combine like terms: 2.4x2 + -2.4x2 = 0.0 -60 + 24x + -2.4x2 = 0.0 Begin completing the square. Divide all terms by -2.4 the coefficient of the squared term: Divide each side by '-2.4'. 25 + -10x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -10x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -10x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -10x + x2 = 0 + -25 -10x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -10x + x2 = -25 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -25 + 25 Reorder the terms: 25 + -10x + x2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + -10x + x2 = 0 Factor a perfect square on the left side: (x + -5)(x + -5) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -5) equal to 0 and 0.Subproblem 1
x + -5 = 0 Simplifying x + -5 = 0 Reorder the terms: -5 + x = 0 Solving -5 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -5 = 0 Simplifying x + -5 = 0 Reorder the terms: -5 + x = 0 Solving -5 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, 5}
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