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Simplifying 2x2 + 20x + -46 = 0 Reorder the terms: -46 + 20x + 2x2 = 0 Solving -46 + 20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-23 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + 10x + x2)' equal to zero and attempt to solve: Simplifying -23 + 10x + x2 = 0 Solving -23 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 10x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 10x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 10x + x2 = 0 + 23 10x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 10x + x2 = 23 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 23 + 25 Reorder the terms: 25 + 10x + x2 = 23 + 25 Combine like terms: 23 + 25 = 48 25 + 10x + x2 = 48 Factor a perfect square on the left side: (x + 5)(x + 5) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + 5) equal to 6.92820323 and -6.92820323.Subproblem 1
x + 5 = 6.92820323 Simplifying x + 5 = 6.92820323 Reorder the terms: 5 + x = 6.92820323 Solving 5 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 6.92820323 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.92820323 + -5 x = 6.92820323 + -5 Combine like terms: 6.92820323 + -5 = 1.92820323 x = 1.92820323 Simplifying x = 1.92820323Subproblem 2
x + 5 = -6.92820323 Simplifying x + 5 = -6.92820323 Reorder the terms: 5 + x = -6.92820323 Solving 5 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -6.92820323 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.92820323 + -5 x = -6.92820323 + -5 Combine like terms: -6.92820323 + -5 = -11.92820323 x = -11.92820323 Simplifying x = -11.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.92820323, -11.92820323}Solution
x = {1.92820323, -11.92820323}
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