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Simplifying x2 + 9.13x + -148 = 0 Reorder the terms: -148 + 9.13x + x2 = 0 Solving -148 + 9.13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '148' to each side of the equation. -148 + 9.13x + 148 + x2 = 0 + 148 Reorder the terms: -148 + 148 + 9.13x + x2 = 0 + 148 Combine like terms: -148 + 148 = 0 0 + 9.13x + x2 = 0 + 148 9.13x + x2 = 0 + 148 Combine like terms: 0 + 148 = 148 9.13x + x2 = 148 The x term is 9.13x. Take half its coefficient (4.565). Square it (20.839225) and add it to both sides. Add '20.839225' to each side of the equation. 9.13x + 20.839225 + x2 = 148 + 20.839225 Reorder the terms: 20.839225 + 9.13x + x2 = 148 + 20.839225 Combine like terms: 148 + 20.839225 = 168.839225 20.839225 + 9.13x + x2 = 168.839225 Factor a perfect square on the left side: (x + 4.565)(x + 4.565) = 168.839225 Calculate the square root of the right side: 12.993814875 Break this problem into two subproblems by setting (x + 4.565) equal to 12.993814875 and -12.993814875.Subproblem 1
x + 4.565 = 12.993814875 Simplifying x + 4.565 = 12.993814875 Reorder the terms: 4.565 + x = 12.993814875 Solving 4.565 + x = 12.993814875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.565' to each side of the equation. 4.565 + -4.565 + x = 12.993814875 + -4.565 Combine like terms: 4.565 + -4.565 = 0.000 0.000 + x = 12.993814875 + -4.565 x = 12.993814875 + -4.565 Combine like terms: 12.993814875 + -4.565 = 8.428814875 x = 8.428814875 Simplifying x = 8.428814875Subproblem 2
x + 4.565 = -12.993814875 Simplifying x + 4.565 = -12.993814875 Reorder the terms: 4.565 + x = -12.993814875 Solving 4.565 + x = -12.993814875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.565' to each side of the equation. 4.565 + -4.565 + x = -12.993814875 + -4.565 Combine like terms: 4.565 + -4.565 = 0.000 0.000 + x = -12.993814875 + -4.565 x = -12.993814875 + -4.565 Combine like terms: -12.993814875 + -4.565 = -17.558814875 x = -17.558814875 Simplifying x = -17.558814875Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.428814875, -17.558814875}
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