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Simplifying 2X2 + 2X + -54 = 0 Reorder the terms: -54 + 2X + 2X2 = 0 Solving -54 + 2X + 2X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + X + X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + X + X2)' equal to zero and attempt to solve: Simplifying -27 + X + X2 = 0 Solving -27 + X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + X + 27 + X2 = 0 + 27 Reorder the terms: -27 + 27 + X + X2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + X + X2 = 0 + 27 X + X2 = 0 + 27 Combine like terms: 0 + 27 = 27 X + X2 = 27 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 = 27 + 0.25 Reorder the terms: 0.25 + X + X2 = 27 + 0.25 Combine like terms: 27 + 0.25 = 27.25 0.25 + X + X2 = 27.25 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (X + 0.5) equal to 5.220153254 and -5.220153254.Subproblem 1
X + 0.5 = 5.220153254 Simplifying X + 0.5 = 5.220153254 Reorder the terms: 0.5 + X = 5.220153254 Solving 0.5 + X = 5.220153254 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 = 5.220153254 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 5.220153254 + -0.5 X = 5.220153254 + -0.5 Combine like terms: 5.220153254 + -0.5 = 4.720153254 X = 4.720153254 Simplifying X = 4.720153254Subproblem 2
X + 0.5 = -5.220153254 Simplifying X + 0.5 = -5.220153254 Reorder the terms: 0.5 + X = -5.220153254 Solving 0.5 + X = -5.220153254 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 = -5.220153254 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -5.220153254 + -0.5 X = -5.220153254 + -0.5 Combine like terms: -5.220153254 + -0.5 = -5.720153254 X = -5.720153254 Simplifying X = -5.720153254Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.720153254, -5.720153254}Solution
X = {4.720153254, -5.720153254}
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