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Simplifying 2x2 + -9x + -78 = 0 Reorder the terms: -78 + -9x + 2x2 = 0 Solving -78 + -9x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -39 + -4.5x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + -4.5x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -4.5x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -4.5x + x2 = 0 + 39 -4.5x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -4.5x + x2 = 39 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 39 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 39 + 5.0625 Combine like terms: 39 + 5.0625 = 44.0625 5.0625 + -4.5x + x2 = 44.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 44.0625 Calculate the square root of the right side: 6.637959024 Break this problem into two subproblems by setting (x + -2.25) equal to 6.637959024 and -6.637959024.Subproblem 1
x + -2.25 = 6.637959024 Simplifying x + -2.25 = 6.637959024 Reorder the terms: -2.25 + x = 6.637959024 Solving -2.25 + x = 6.637959024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 6.637959024 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 6.637959024 + 2.25 x = 6.637959024 + 2.25 Combine like terms: 6.637959024 + 2.25 = 8.887959024 x = 8.887959024 Simplifying x = 8.887959024Subproblem 2
x + -2.25 = -6.637959024 Simplifying x + -2.25 = -6.637959024 Reorder the terms: -2.25 + x = -6.637959024 Solving -2.25 + x = -6.637959024 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -6.637959024 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -6.637959024 + 2.25 x = -6.637959024 + 2.25 Combine like terms: -6.637959024 + 2.25 = -4.387959024 x = -4.387959024 Simplifying x = -4.387959024Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.887959024, -4.387959024}
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