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Simplifying 2x2 + 6x + -32 = 0 Reorder the terms: -32 + 6x + 2x2 = 0 Solving -32 + 6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + 3x + x2)' equal to zero and attempt to solve: Simplifying -16 + 3x + x2 = 0 Solving -16 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 3x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 3x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 3x + x2 = 0 + 16 3x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 3x + x2 = 16 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 16 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 16 + 2.25 Combine like terms: 16 + 2.25 = 18.25 2.25 + 3x + x2 = 18.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + 1.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + 1.5 = 4.272001873 Simplifying x + 1.5 = 4.272001873 Reorder the terms: 1.5 + x = 4.272001873 Solving 1.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.272001873 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.272001873 + -1.5 x = 4.272001873 + -1.5 Combine like terms: 4.272001873 + -1.5 = 2.772001873 x = 2.772001873 Simplifying x = 2.772001873Subproblem 2
x + 1.5 = -4.272001873 Simplifying x + 1.5 = -4.272001873 Reorder the terms: 1.5 + x = -4.272001873 Solving 1.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.272001873 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.272001873 + -1.5 x = -4.272001873 + -1.5 Combine like terms: -4.272001873 + -1.5 = -5.772001873 x = -5.772001873 Simplifying x = -5.772001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.772001873, -5.772001873}Solution
x = {2.772001873, -5.772001873}
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