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Simplifying 2x2 + 2x + -6 = 30 Reorder the terms: -6 + 2x + 2x2 = 30 Solving -6 + 2x + 2x2 = 30 Solving for variable 'x'. Reorder the terms: -6 + -30 + 2x + 2x2 = 30 + -30 Combine like terms: -6 + -30 = -36 -36 + 2x + 2x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -36 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + x + x2)' equal to zero and attempt to solve: Simplifying -18 + x + x2 = 0 Solving -18 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + x + x2 = 0 + 18 x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 x + x2 = 18 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 18 + 0.25 Reorder the terms: 0.25 + x + x2 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 0.25 + x + x2 = 18.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + 0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + 0.5 = 4.272001873 Simplifying x + 0.5 = 4.272001873 Reorder the terms: 0.5 + x = 4.272001873 Solving 0.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.272001873 + -0.5 x = 4.272001873 + -0.5 Combine like terms: 4.272001873 + -0.5 = 3.772001873 x = 3.772001873 Simplifying x = 3.772001873Subproblem 2
x + 0.5 = -4.272001873 Simplifying x + 0.5 = -4.272001873 Reorder the terms: 0.5 + x = -4.272001873 Solving 0.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.272001873 + -0.5 x = -4.272001873 + -0.5 Combine like terms: -4.272001873 + -0.5 = -4.772001873 x = -4.772001873 Simplifying x = -4.772001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.772001873, -4.772001873}Solution
x = {3.772001873, -4.772001873}
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