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Simplifying 0 = x2 + -3x + -44 Reorder the terms: 0 = -44 + -3x + x2 Solving 0 = -44 + -3x + x2 Solving for variable 'x'. Combine like terms: 0 + 44 = 44 44 + 3x + -1x2 = -44 + -3x + x2 + 44 + 3x + -1x2 Reorder the terms: 44 + 3x + -1x2 = -44 + 44 + -3x + 3x + x2 + -1x2 Combine like terms: -44 + 44 = 0 44 + 3x + -1x2 = 0 + -3x + 3x + x2 + -1x2 44 + 3x + -1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 44 + 3x + -1x2 = 0 + x2 + -1x2 44 + 3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 44 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -44 + -3x + x2 = 0 Move the constant term to the right: Add '44' to each side of the equation. -44 + -3x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + -3x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -3x + x2 = 0 + 44 -3x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 -3x + x2 = 44 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 44 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 44 + 2.25 Combine like terms: 44 + 2.25 = 46.25 2.25 + -3x + x2 = 46.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (x + -1.5) equal to 6.800735254 and -6.800735254.Subproblem 1
x + -1.5 = 6.800735254 Simplifying x + -1.5 = 6.800735254 Reorder the terms: -1.5 + x = 6.800735254 Solving -1.5 + x = 6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.800735254 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.800735254 + 1.5 x = 6.800735254 + 1.5 Combine like terms: 6.800735254 + 1.5 = 8.300735254 x = 8.300735254 Simplifying x = 8.300735254Subproblem 2
x + -1.5 = -6.800735254 Simplifying x + -1.5 = -6.800735254 Reorder the terms: -1.5 + x = -6.800735254 Solving -1.5 + x = -6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.800735254 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.800735254 + 1.5 x = -6.800735254 + 1.5 Combine like terms: -6.800735254 + 1.5 = -5.300735254 x = -5.300735254 Simplifying x = -5.300735254Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.300735254, -5.300735254}
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