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Simplifying 4X2 + 8X + -180 = 0 Reorder the terms: -180 + 8X + 4X2 = 0 Solving -180 + 8X + 4X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + 2X + X2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-45 + 2X + X2)' equal to zero and attempt to solve: Simplifying -45 + 2X + X2 = 0 Solving -45 + 2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 2X + 45 + X2 = 0 + 45 Reorder the terms: -45 + 45 + 2X + X2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 2X + X2 = 0 + 45 2X + X2 = 0 + 45 Combine like terms: 0 + 45 = 45 2X + X2 = 45 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 = 45 + 1 Reorder the terms: 1 + 2X + X2 = 45 + 1 Combine like terms: 45 + 1 = 46 1 + 2X + X2 = 46 Factor a perfect square on the left side: (X + 1)(X + 1) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (X + 1) equal to 6.782329983 and -6.782329983.Subproblem 1
X + 1 = 6.782329983 Simplifying X + 1 = 6.782329983 Reorder the terms: 1 + X = 6.782329983 Solving 1 + X = 6.782329983 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 = 6.782329983 + -1 Combine like terms: 1 + -1 = 0 0 + X = 6.782329983 + -1 X = 6.782329983 + -1 Combine like terms: 6.782329983 + -1 = 5.782329983 X = 5.782329983 Simplifying X = 5.782329983Subproblem 2
X + 1 = -6.782329983 Simplifying X + 1 = -6.782329983 Reorder the terms: 1 + X = -6.782329983 Solving 1 + X = -6.782329983 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 = -6.782329983 + -1 Combine like terms: 1 + -1 = 0 0 + X = -6.782329983 + -1 X = -6.782329983 + -1 Combine like terms: -6.782329983 + -1 = -7.782329983 X = -7.782329983 Simplifying X = -7.782329983Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.782329983, -7.782329983}Solution
X = {5.782329983, -7.782329983}
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