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Simplifying 0 = 2x2 + -3x + -38 Reorder the terms: 0 = -38 + -3x + 2x2 Solving 0 = -38 + -3x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 38 = 38 38 + 3x + -2x2 = -38 + -3x + 2x2 + 38 + 3x + -2x2 Reorder the terms: 38 + 3x + -2x2 = -38 + 38 + -3x + 3x + 2x2 + -2x2 Combine like terms: -38 + 38 = 0 38 + 3x + -2x2 = 0 + -3x + 3x + 2x2 + -2x2 38 + 3x + -2x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 38 + 3x + -2x2 = 0 + 2x2 + -2x2 38 + 3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 38 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -19 + -1.5x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + -1.5x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -1.5x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -1.5x + x2 = 0 + 19 -1.5x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -1.5x + x2 = 19 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 19 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 19 + 0.5625 Combine like terms: 19 + 0.5625 = 19.5625 0.5625 + -1.5x + x2 = 19.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 19.5625 Calculate the square root of the right side: 4.422951503 Break this problem into two subproblems by setting (x + -0.75) equal to 4.422951503 and -4.422951503.Subproblem 1
x + -0.75 = 4.422951503 Simplifying x + -0.75 = 4.422951503 Reorder the terms: -0.75 + x = 4.422951503 Solving -0.75 + x = 4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 4.422951503 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 4.422951503 + 0.75 x = 4.422951503 + 0.75 Combine like terms: 4.422951503 + 0.75 = 5.172951503 x = 5.172951503 Simplifying x = 5.172951503Subproblem 2
x + -0.75 = -4.422951503 Simplifying x + -0.75 = -4.422951503 Reorder the terms: -0.75 + x = -4.422951503 Solving -0.75 + x = -4.422951503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -4.422951503 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -4.422951503 + 0.75 x = -4.422951503 + 0.75 Combine like terms: -4.422951503 + 0.75 = -3.672951503 x = -3.672951503 Simplifying x = -3.672951503Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.172951503, -3.672951503}
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