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Simplifying 111 = x2 + 48x Reorder the terms: 111 = 48x + x2 Solving 111 = 48x + x2 Solving for variable 'x'. Reorder the terms: 111 + -48x + -1x2 = 48x + -48x + x2 + -1x2 Combine like terms: 48x + -48x = 0 111 + -48x + -1x2 = 0 + x2 + -1x2 111 + -48x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 111 + -48x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -111 + 48x + x2 = 0 Move the constant term to the right: Add '111' to each side of the equation. -111 + 48x + 111 + x2 = 0 + 111 Reorder the terms: -111 + 111 + 48x + x2 = 0 + 111 Combine like terms: -111 + 111 = 0 0 + 48x + x2 = 0 + 111 48x + x2 = 0 + 111 Combine like terms: 0 + 111 = 111 48x + x2 = 111 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 = 111 + 576 Reorder the terms: 576 + 48x + x2 = 111 + 576 Combine like terms: 111 + 576 = 687 576 + 48x + x2 = 687 Factor a perfect square on the left side: (x + 24)(x + 24) = 687 Calculate the square root of the right side: 26.210684844 Break this problem into two subproblems by setting (x + 24) equal to 26.210684844 and -26.210684844.Subproblem 1
x + 24 = 26.210684844 Simplifying x + 24 = 26.210684844 Reorder the terms: 24 + x = 26.210684844 Solving 24 + x = 26.210684844 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 = 26.210684844 + -24 Combine like terms: 24 + -24 = 0 0 + x = 26.210684844 + -24 x = 26.210684844 + -24 Combine like terms: 26.210684844 + -24 = 2.210684844 x = 2.210684844 Simplifying x = 2.210684844Subproblem 2
x + 24 = -26.210684844 Simplifying x + 24 = -26.210684844 Reorder the terms: 24 + x = -26.210684844 Solving 24 + x = -26.210684844 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 = -26.210684844 + -24 Combine like terms: 24 + -24 = 0 0 + x = -26.210684844 + -24 x = -26.210684844 + -24 Combine like terms: -26.210684844 + -24 = -50.210684844 x = -50.210684844 Simplifying x = -50.210684844Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.210684844, -50.210684844}
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