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Simplifying 2x2 + -54x + 4 = 0 Reorder the terms: 4 + -54x + 2x2 = 0 Solving 4 + -54x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -27x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -27x + x2)' equal to zero and attempt to solve: Simplifying 2 + -27x + x2 = 0 Solving 2 + -27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -27x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -27x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -27x + x2 = 0 + -2 -27x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -27x + x2 = -2 The x term is -27x. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27x + 182.25 + x2 = -2 + 182.25 Reorder the terms: 182.25 + -27x + x2 = -2 + 182.25 Combine like terms: -2 + 182.25 = 180.25 182.25 + -27x + x2 = 180.25 Factor a perfect square on the left side: (x + -13.5)(x + -13.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + -13.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + -13.5 = 13.425721582 Simplifying x + -13.5 = 13.425721582 Reorder the terms: -13.5 + x = 13.425721582 Solving -13.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 13.425721582 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 13.425721582 + 13.5 x = 13.425721582 + 13.5 Combine like terms: 13.425721582 + 13.5 = 26.925721582 x = 26.925721582 Simplifying x = 26.925721582Subproblem 2
x + -13.5 = -13.425721582 Simplifying x + -13.5 = -13.425721582 Reorder the terms: -13.5 + x = -13.425721582 Solving -13.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -13.425721582 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -13.425721582 + 13.5 x = -13.425721582 + 13.5 Combine like terms: -13.425721582 + 13.5 = 0.074278418 x = 0.074278418 Simplifying x = 0.074278418Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.925721582, 0.074278418}Solution
x = {26.925721582, 0.074278418}
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