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Simplifying x * x + 5x + -12 = 22 Multiply x * x x2 + 5x + -12 = 22 Reorder the terms: -12 + 5x + x2 = 22 Solving -12 + 5x + x2 = 22 Solving for variable 'x'. Reorder the terms: -12 + -22 + 5x + x2 = 22 + -22 Combine like terms: -12 + -22 = -34 -34 + 5x + x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -34 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 5x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + 5x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 5x + x2 = 0 + 34 5x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 5x + x2 = 34 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 34 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 34 + 6.25 Combine like terms: 34 + 6.25 = 40.25 6.25 + 5x + x2 = 40.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + 2.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + 2.5 = 6.34428877 Simplifying x + 2.5 = 6.34428877 Reorder the terms: 2.5 + x = 6.34428877 Solving 2.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 6.34428877 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.34428877 + -2.5 x = 6.34428877 + -2.5 Combine like terms: 6.34428877 + -2.5 = 3.84428877 x = 3.84428877 Simplifying x = 3.84428877Subproblem 2
x + 2.5 = -6.34428877 Simplifying x + 2.5 = -6.34428877 Reorder the terms: 2.5 + x = -6.34428877 Solving 2.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -6.34428877 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.34428877 + -2.5 x = -6.34428877 + -2.5 Combine like terms: -6.34428877 + -2.5 = -8.84428877 x = -8.84428877 Simplifying x = -8.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.84428877, -8.84428877}
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