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Simplifying x2 + 6x + -24.01 = 0 Reorder the terms: -24.01 + 6x + x2 = 0 Solving -24.01 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '24.01' to each side of the equation. -24.01 + 6x + 24.01 + x2 = 0 + 24.01 Reorder the terms: -24.01 + 24.01 + 6x + x2 = 0 + 24.01 Combine like terms: -24.01 + 24.01 = 0.00 0.00 + 6x + x2 = 0 + 24.01 6x + x2 = 0 + 24.01 Combine like terms: 0 + 24.01 = 24.01 6x + x2 = 24.01 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 24.01 + 9 Reorder the terms: 9 + 6x + x2 = 24.01 + 9 Combine like terms: 24.01 + 9 = 33.01 9 + 6x + x2 = 33.01 Factor a perfect square on the left side: (x + 3)(x + 3) = 33.01 Calculate the square root of the right side: 5.745432969 Break this problem into two subproblems by setting (x + 3) equal to 5.745432969 and -5.745432969.Subproblem 1
x + 3 = 5.745432969 Simplifying x + 3 = 5.745432969 Reorder the terms: 3 + x = 5.745432969 Solving 3 + x = 5.745432969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.745432969 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.745432969 + -3 x = 5.745432969 + -3 Combine like terms: 5.745432969 + -3 = 2.745432969 x = 2.745432969 Simplifying x = 2.745432969Subproblem 2
x + 3 = -5.745432969 Simplifying x + 3 = -5.745432969 Reorder the terms: 3 + x = -5.745432969 Solving 3 + x = -5.745432969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.745432969 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.745432969 + -3 x = -5.745432969 + -3 Combine like terms: -5.745432969 + -3 = -8.745432969 x = -8.745432969 Simplifying x = -8.745432969Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.745432969, -8.745432969}
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