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Simplifying 2x2 + 12x + -38 = 0 Reorder the terms: -38 + 12x + 2x2 = 0 Solving -38 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + 6x + x2)' equal to zero and attempt to solve: Simplifying -19 + 6x + x2 = 0 Solving -19 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 6x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 6x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 6x + x2 = 0 + 19 6x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 6x + x2 = 19 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 19 + 9 Reorder the terms: 9 + 6x + x2 = 19 + 9 Combine like terms: 19 + 9 = 28 9 + 6x + x2 = 28 Factor a perfect square on the left side: (x + 3)(x + 3) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + 3) equal to 5.291502622 and -5.291502622.Subproblem 1
x + 3 = 5.291502622 Simplifying x + 3 = 5.291502622 Reorder the terms: 3 + x = 5.291502622 Solving 3 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.291502622 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.291502622 + -3 x = 5.291502622 + -3 Combine like terms: 5.291502622 + -3 = 2.291502622 x = 2.291502622 Simplifying x = 2.291502622Subproblem 2
x + 3 = -5.291502622 Simplifying x + 3 = -5.291502622 Reorder the terms: 3 + x = -5.291502622 Solving 3 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.291502622 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.291502622 + -3 x = -5.291502622 + -3 Combine like terms: -5.291502622 + -3 = -8.291502622 x = -8.291502622 Simplifying x = -8.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.291502622, -8.291502622}Solution
x = {2.291502622, -8.291502622}
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