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Simplifying 2x2 + 9x = 351 Reorder the terms: 9x + 2x2 = 351 Solving 9x + 2x2 = 351 Solving for variable 'x'. Reorder the terms: -351 + 9x + 2x2 = 351 + -351 Combine like terms: 351 + -351 = 0 -351 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -175.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '175.5' to each side of the equation. -175.5 + 4.5x + 175.5 + x2 = 0 + 175.5 Reorder the terms: -175.5 + 175.5 + 4.5x + x2 = 0 + 175.5 Combine like terms: -175.5 + 175.5 = 0.0 0.0 + 4.5x + x2 = 0 + 175.5 4.5x + x2 = 0 + 175.5 Combine like terms: 0 + 175.5 = 175.5 4.5x + x2 = 175.5 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 = 175.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 175.5 + 5.0625 Combine like terms: 175.5 + 5.0625 = 180.5625 5.0625 + 4.5x + x2 = 180.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 180.5625 Calculate the square root of the right side: 13.43735465 Break this problem into two subproblems by setting (x + 2.25) equal to 13.43735465 and -13.43735465.Subproblem 1
x + 2.25 = 13.43735465 Simplifying x + 2.25 = 13.43735465 Reorder the terms: 2.25 + x = 13.43735465 Solving 2.25 + x = 13.43735465 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 = 13.43735465 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 13.43735465 + -2.25 x = 13.43735465 + -2.25 Combine like terms: 13.43735465 + -2.25 = 11.18735465 x = 11.18735465 Simplifying x = 11.18735465Subproblem 2
x + 2.25 = -13.43735465 Simplifying x + 2.25 = -13.43735465 Reorder the terms: 2.25 + x = -13.43735465 Solving 2.25 + x = -13.43735465 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 = -13.43735465 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -13.43735465 + -2.25 x = -13.43735465 + -2.25 Combine like terms: -13.43735465 + -2.25 = -15.68735465 x = -15.68735465 Simplifying x = -15.68735465Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.18735465, -15.68735465}
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