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Simplifying 2x2 + 4x + -450 = 0 Reorder the terms: -450 + 4x + 2x2 = 0 Solving -450 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-225 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-225 + 2x + x2)' equal to zero and attempt to solve: Simplifying -225 + 2x + x2 = 0 Solving -225 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 2x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 2x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 2x + x2 = 0 + 225 2x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 2x + x2 = 225 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 225 + 1 Reorder the terms: 1 + 2x + x2 = 225 + 1 Combine like terms: 225 + 1 = 226 1 + 2x + x2 = 226 Factor a perfect square on the left side: (x + 1)(x + 1) = 226 Calculate the square root of the right side: 15.033296378 Break this problem into two subproblems by setting (x + 1) equal to 15.033296378 and -15.033296378.Subproblem 1
x + 1 = 15.033296378 Simplifying x + 1 = 15.033296378 Reorder the terms: 1 + x = 15.033296378 Solving 1 + x = 15.033296378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 15.033296378 + -1 Combine like terms: 1 + -1 = 0 0 + x = 15.033296378 + -1 x = 15.033296378 + -1 Combine like terms: 15.033296378 + -1 = 14.033296378 x = 14.033296378 Simplifying x = 14.033296378Subproblem 2
x + 1 = -15.033296378 Simplifying x + 1 = -15.033296378 Reorder the terms: 1 + x = -15.033296378 Solving 1 + x = -15.033296378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -15.033296378 + -1 Combine like terms: 1 + -1 = 0 0 + x = -15.033296378 + -1 x = -15.033296378 + -1 Combine like terms: -15.033296378 + -1 = -16.033296378 x = -16.033296378 Simplifying x = -16.033296378Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.033296378, -16.033296378}Solution
x = {14.033296378, -16.033296378}
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