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Simplifying 0 = x2 + 5x + -12 Reorder the terms: 0 = -12 + 5x + x2 Solving 0 = -12 + 5x + x2 Solving for variable 'x'. Combine like terms: 0 + 12 = 12 12 + -5x + -1x2 = -12 + 5x + x2 + 12 + -5x + -1x2 Reorder the terms: 12 + -5x + -1x2 = -12 + 12 + 5x + -5x + x2 + -1x2 Combine like terms: -12 + 12 = 0 12 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 12 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 12 + -5x + -1x2 = 0 + x2 + -1x2 12 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + 5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 5x + x2 = 0 + 12 5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 5x + x2 = 12 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 = 12 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 12 + 6.25 Combine like terms: 12 + 6.25 = 18.25 6.25 + 5x + x2 = 18.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + 2.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + 2.5 = 4.272001873 Simplifying x + 2.5 = 4.272001873 Reorder the terms: 2.5 + x = 4.272001873 Solving 2.5 + x = 4.272001873 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 = 4.272001873 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.272001873 + -2.5 x = 4.272001873 + -2.5 Combine like terms: 4.272001873 + -2.5 = 1.772001873 x = 1.772001873 Simplifying x = 1.772001873Subproblem 2
x + 2.5 = -4.272001873 Simplifying x + 2.5 = -4.272001873 Reorder the terms: 2.5 + x = -4.272001873 Solving 2.5 + x = -4.272001873 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 = -4.272001873 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.272001873 + -2.5 x = -4.272001873 + -2.5 Combine like terms: -4.272001873 + -2.5 = -6.772001873 x = -6.772001873 Simplifying x = -6.772001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.772001873, -6.772001873}
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