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Simplifying 0 = -0.025x2 + 3.6x + -98.8 Reorder the terms: 0 = -98.8 + 3.6x + -0.025x2 Solving 0 = -98.8 + 3.6x + -0.025x2 Solving for variable 'x'. Combine like terms: 0 + 98.8 = 98.8 98.8 + -3.6x + 0.025x2 = -98.8 + 3.6x + -0.025x2 + 98.8 + -3.6x + 0.025x2 Reorder the terms: 98.8 + -3.6x + 0.025x2 = -98.8 + 98.8 + 3.6x + -3.6x + -0.025x2 + 0.025x2 Combine like terms: -98.8 + 98.8 = 0.0 98.8 + -3.6x + 0.025x2 = 0.0 + 3.6x + -3.6x + -0.025x2 + 0.025x2 98.8 + -3.6x + 0.025x2 = 3.6x + -3.6x + -0.025x2 + 0.025x2 Combine like terms: 3.6x + -3.6x = 0.0 98.8 + -3.6x + 0.025x2 = 0.0 + -0.025x2 + 0.025x2 98.8 + -3.6x + 0.025x2 = -0.025x2 + 0.025x2 Combine like terms: -0.025x2 + 0.025x2 = 0.000 98.8 + -3.6x + 0.025x2 = 0.000 Begin completing the square. Divide all terms by 0.025 the coefficient of the squared term: Divide each side by '0.025'. 3952 + -144x + x2 = 0 Move the constant term to the right: Add '-3952' to each side of the equation. 3952 + -144x + -3952 + x2 = 0 + -3952 Reorder the terms: 3952 + -3952 + -144x + x2 = 0 + -3952 Combine like terms: 3952 + -3952 = 0 0 + -144x + x2 = 0 + -3952 -144x + x2 = 0 + -3952 Combine like terms: 0 + -3952 = -3952 -144x + x2 = -3952 The x term is -144x. Take half its coefficient (-72). Square it (5184) and add it to both sides. Add '5184' to each side of the equation. -144x + 5184 + x2 = -3952 + 5184 Reorder the terms: 5184 + -144x + x2 = -3952 + 5184 Combine like terms: -3952 + 5184 = 1232 5184 + -144x + x2 = 1232 Factor a perfect square on the left side: (x + -72)(x + -72) = 1232 Calculate the square root of the right side: 35.09985755 Break this problem into two subproblems by setting (x + -72) equal to 35.09985755 and -35.09985755.Subproblem 1
x + -72 = 35.09985755 Simplifying x + -72 = 35.09985755 Reorder the terms: -72 + x = 35.09985755 Solving -72 + x = 35.09985755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '72' to each side of the equation. -72 + 72 + x = 35.09985755 + 72 Combine like terms: -72 + 72 = 0 0 + x = 35.09985755 + 72 x = 35.09985755 + 72 Combine like terms: 35.09985755 + 72 = 107.09985755 x = 107.09985755 Simplifying x = 107.09985755Subproblem 2
x + -72 = -35.09985755 Simplifying x + -72 = -35.09985755 Reorder the terms: -72 + x = -35.09985755 Solving -72 + x = -35.09985755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '72' to each side of the equation. -72 + 72 + x = -35.09985755 + 72 Combine like terms: -72 + 72 = 0 0 + x = -35.09985755 + 72 x = -35.09985755 + 72 Combine like terms: -35.09985755 + 72 = 36.90014245 x = 36.90014245 Simplifying x = 36.90014245Solution
The solution to the problem is based on the solutions from the subproblems. x = {107.09985755, 36.90014245}
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