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Simplifying 2x2 + -9x = 89 Reorder the terms: -9x + 2x2 = 89 Solving -9x + 2x2 = 89 Solving for variable 'x'. Reorder the terms: -89 + -9x + 2x2 = 89 + -89 Combine like terms: 89 + -89 = 0 -89 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -44.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '44.5' to each side of the equation. -44.5 + -4.5x + 44.5 + x2 = 0 + 44.5 Reorder the terms: -44.5 + 44.5 + -4.5x + x2 = 0 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + -4.5x + x2 = 0 + 44.5 -4.5x + x2 = 0 + 44.5 Combine like terms: 0 + 44.5 = 44.5 -4.5x + x2 = 44.5 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 = 44.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 44.5 + 5.0625 Combine like terms: 44.5 + 5.0625 = 49.5625 5.0625 + -4.5x + x2 = 49.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 49.5625 Calculate the square root of the right side: 7.04006392 Break this problem into two subproblems by setting (x + -2.25) equal to 7.04006392 and -7.04006392.Subproblem 1
x + -2.25 = 7.04006392 Simplifying x + -2.25 = 7.04006392 Reorder the terms: -2.25 + x = 7.04006392 Solving -2.25 + x = 7.04006392 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 = 7.04006392 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 7.04006392 + 2.25 x = 7.04006392 + 2.25 Combine like terms: 7.04006392 + 2.25 = 9.29006392 x = 9.29006392 Simplifying x = 9.29006392Subproblem 2
x + -2.25 = -7.04006392 Simplifying x + -2.25 = -7.04006392 Reorder the terms: -2.25 + x = -7.04006392 Solving -2.25 + x = -7.04006392 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 = -7.04006392 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -7.04006392 + 2.25 x = -7.04006392 + 2.25 Combine like terms: -7.04006392 + 2.25 = -4.79006392 x = -4.79006392 Simplifying x = -4.79006392Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.29006392, -4.79006392}
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