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Simplifying 2x2 + 8x + -598 = 0 Reorder the terms: -598 + 8x + 2x2 = 0 Solving -598 + 8x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-299 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-299 + 4x + x2)' equal to zero and attempt to solve: Simplifying -299 + 4x + x2 = 0 Solving -299 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '299' to each side of the equation. -299 + 4x + 299 + x2 = 0 + 299 Reorder the terms: -299 + 299 + 4x + x2 = 0 + 299 Combine like terms: -299 + 299 = 0 0 + 4x + x2 = 0 + 299 4x + x2 = 0 + 299 Combine like terms: 0 + 299 = 299 4x + x2 = 299 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 299 + 4 Reorder the terms: 4 + 4x + x2 = 299 + 4 Combine like terms: 299 + 4 = 303 4 + 4x + x2 = 303 Factor a perfect square on the left side: (x + 2)(x + 2) = 303 Calculate the square root of the right side: 17.406895186 Break this problem into two subproblems by setting (x + 2) equal to 17.406895186 and -17.406895186.Subproblem 1
x + 2 = 17.406895186 Simplifying x + 2 = 17.406895186 Reorder the terms: 2 + x = 17.406895186 Solving 2 + x = 17.406895186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 17.406895186 + -2 Combine like terms: 2 + -2 = 0 0 + x = 17.406895186 + -2 x = 17.406895186 + -2 Combine like terms: 17.406895186 + -2 = 15.406895186 x = 15.406895186 Simplifying x = 15.406895186Subproblem 2
x + 2 = -17.406895186 Simplifying x + 2 = -17.406895186 Reorder the terms: 2 + x = -17.406895186 Solving 2 + x = -17.406895186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -17.406895186 + -2 Combine like terms: 2 + -2 = 0 0 + x = -17.406895186 + -2 x = -17.406895186 + -2 Combine like terms: -17.406895186 + -2 = -19.406895186 x = -19.406895186 Simplifying x = -19.406895186Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.406895186, -19.406895186}Solution
x = {15.406895186, -19.406895186}
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