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Simplifying 2x2 + 4x = 54 Reorder the terms: 4x + 2x2 = 54 Solving 4x + 2x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + 4x + 2x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + 2x + x2)' equal to zero and attempt to solve: Simplifying -27 + 2x + x2 = 0 Solving -27 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 2x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 2x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 2x + x2 = 0 + 27 2x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 2x + x2 = 27 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 = 27 + 1 Reorder the terms: 1 + 2x + x2 = 27 + 1 Combine like terms: 27 + 1 = 28 1 + 2x + x2 = 28 Factor a perfect square on the left side: (x + 1)(x + 1) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + 1) equal to 5.291502622 and -5.291502622.Subproblem 1
x + 1 = 5.291502622 Simplifying x + 1 = 5.291502622 Reorder the terms: 1 + x = 5.291502622 Solving 1 + x = 5.291502622 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 = 5.291502622 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.291502622 + -1 x = 5.291502622 + -1 Combine like terms: 5.291502622 + -1 = 4.291502622 x = 4.291502622 Simplifying x = 4.291502622Subproblem 2
x + 1 = -5.291502622 Simplifying x + 1 = -5.291502622 Reorder the terms: 1 + x = -5.291502622 Solving 1 + x = -5.291502622 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 = -5.291502622 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.291502622 + -1 x = -5.291502622 + -1 Combine like terms: -5.291502622 + -1 = -6.291502622 x = -6.291502622 Simplifying x = -6.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.291502622, -6.291502622}Solution
x = {4.291502622, -6.291502622}
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