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Simplifying 0 = x2 + 48x + -144 Reorder the terms: 0 = -144 + 48x + x2 Solving 0 = -144 + 48x + x2 Solving for variable 'x'. Combine like terms: 0 + 144 = 144 144 + -48x + -1x2 = -144 + 48x + x2 + 144 + -48x + -1x2 Reorder the terms: 144 + -48x + -1x2 = -144 + 144 + 48x + -48x + x2 + -1x2 Combine like terms: -144 + 144 = 0 144 + -48x + -1x2 = 0 + 48x + -48x + x2 + -1x2 144 + -48x + -1x2 = 48x + -48x + x2 + -1x2 Combine like terms: 48x + -48x = 0 144 + -48x + -1x2 = 0 + x2 + -1x2 144 + -48x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 144 + -48x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -144 + 48x + x2 = 0 Move the constant term to the right: Add '144' to each side of the equation. -144 + 48x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 48x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 48x + x2 = 0 + 144 48x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 48x + x2 = 144 The x term is 48x. Take half its coefficient (24). Square it (576) and add it to both sides. Add '576' to each side of the equation. 48x + 576 + x2 = 144 + 576 Reorder the terms: 576 + 48x + x2 = 144 + 576 Combine like terms: 144 + 576 = 720 576 + 48x + x2 = 720 Factor a perfect square on the left side: (x + 24)(x + 24) = 720 Calculate the square root of the right side: 26.83281573 Break this problem into two subproblems by setting (x + 24) equal to 26.83281573 and -26.83281573.Subproblem 1
x + 24 = 26.83281573 Simplifying x + 24 = 26.83281573 Reorder the terms: 24 + x = 26.83281573 Solving 24 + x = 26.83281573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = 26.83281573 + -24 Combine like terms: 24 + -24 = 0 0 + x = 26.83281573 + -24 x = 26.83281573 + -24 Combine like terms: 26.83281573 + -24 = 2.83281573 x = 2.83281573 Simplifying x = 2.83281573Subproblem 2
x + 24 = -26.83281573 Simplifying x + 24 = -26.83281573 Reorder the terms: 24 + x = -26.83281573 Solving 24 + x = -26.83281573 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = -26.83281573 + -24 Combine like terms: 24 + -24 = 0 0 + x = -26.83281573 + -24 x = -26.83281573 + -24 Combine like terms: -26.83281573 + -24 = -50.83281573 x = -50.83281573 Simplifying x = -50.83281573Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.83281573, -50.83281573}
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