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Simplifying x2 + 22976x + -21076 = 0 Reorder the terms: -21076 + 22976x + x2 = 0 Solving -21076 + 22976x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '21076' to each side of the equation. -21076 + 22976x + 21076 + x2 = 0 + 21076 Reorder the terms: -21076 + 21076 + 22976x + x2 = 0 + 21076 Combine like terms: -21076 + 21076 = 0 0 + 22976x + x2 = 0 + 21076 22976x + x2 = 0 + 21076 Combine like terms: 0 + 21076 = 21076 22976x + x2 = 21076 The x term is 22976x. Take half its coefficient (11488). Square it (131974144) and add it to both sides. Add '131974144' to each side of the equation. 22976x + 131974144 + x2 = 21076 + 131974144 Reorder the terms: 131974144 + 22976x + x2 = 21076 + 131974144 Combine like terms: 21076 + 131974144 = 131995220 131974144 + 22976x + x2 = 131995220 Factor a perfect square on the left side: (x + 11488)(x + 11488) = 131995220 Calculate the square root of the right side: 11488.917268394 Break this problem into two subproblems by setting (x + 11488) equal to 11488.917268394 and -11488.917268394.Subproblem 1
x + 11488 = 11488.917268394 Simplifying x + 11488 = 11488.917268394 Reorder the terms: 11488 + x = 11488.917268394 Solving 11488 + x = 11488.917268394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11488' to each side of the equation. 11488 + -11488 + x = 11488.917268394 + -11488 Combine like terms: 11488 + -11488 = 0 0 + x = 11488.917268394 + -11488 x = 11488.917268394 + -11488 Combine like terms: 11488.917268394 + -11488 = 0.917268394 x = 0.917268394 Simplifying x = 0.917268394Subproblem 2
x + 11488 = -11488.917268394 Simplifying x + 11488 = -11488.917268394 Reorder the terms: 11488 + x = -11488.917268394 Solving 11488 + x = -11488.917268394 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11488' to each side of the equation. 11488 + -11488 + x = -11488.917268394 + -11488 Combine like terms: 11488 + -11488 = 0 0 + x = -11488.917268394 + -11488 x = -11488.917268394 + -11488 Combine like terms: -11488.917268394 + -11488 = -22976.917268394 x = -22976.917268394 Simplifying x = -22976.917268394Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.917268394, -22976.917268394}
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