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Simplifying x2 + 24x + 23 = 78 Reorder the terms: 23 + 24x + x2 = 78 Solving 23 + 24x + x2 = 78 Solving for variable 'x'. Reorder the terms: 23 + -78 + 24x + x2 = 78 + -78 Combine like terms: 23 + -78 = -55 -55 + 24x + x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -55 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 24x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + 24x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 24x + x2 = 0 + 55 24x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 24x + x2 = 55 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 55 + 144 Reorder the terms: 144 + 24x + x2 = 55 + 144 Combine like terms: 55 + 144 = 199 144 + 24x + x2 = 199 Factor a perfect square on the left side: (x + 12)(x + 12) = 199 Calculate the square root of the right side: 14.10673598 Break this problem into two subproblems by setting (x + 12) equal to 14.10673598 and -14.10673598.Subproblem 1
x + 12 = 14.10673598 Simplifying x + 12 = 14.10673598 Reorder the terms: 12 + x = 14.10673598 Solving 12 + x = 14.10673598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 14.10673598 + -12 Combine like terms: 12 + -12 = 0 0 + x = 14.10673598 + -12 x = 14.10673598 + -12 Combine like terms: 14.10673598 + -12 = 2.10673598 x = 2.10673598 Simplifying x = 2.10673598Subproblem 2
x + 12 = -14.10673598 Simplifying x + 12 = -14.10673598 Reorder the terms: 12 + x = -14.10673598 Solving 12 + x = -14.10673598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -14.10673598 + -12 Combine like terms: 12 + -12 = 0 0 + x = -14.10673598 + -12 x = -14.10673598 + -12 Combine like terms: -14.10673598 + -12 = -26.10673598 x = -26.10673598 Simplifying x = -26.10673598Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.10673598, -26.10673598}
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