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Simplifying 9x + 2x2 = 312 Solving 9x + 2x2 = 312 Solving for variable 'x'. Reorder the terms: -312 + 9x + 2x2 = 312 + -312 Combine like terms: 312 + -312 = 0 -312 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -156 + 4.5x + x2 = 0 Move the constant term to the right: Add '156' to each side of the equation. -156 + 4.5x + 156 + x2 = 0 + 156 Reorder the terms: -156 + 156 + 4.5x + x2 = 0 + 156 Combine like terms: -156 + 156 = 0 0 + 4.5x + x2 = 0 + 156 4.5x + x2 = 0 + 156 Combine like terms: 0 + 156 = 156 4.5x + x2 = 156 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 = 156 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 156 + 5.0625 Combine like terms: 156 + 5.0625 = 161.0625 5.0625 + 4.5x + x2 = 161.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 161.0625 Calculate the square root of the right side: 12.691040146 Break this problem into two subproblems by setting (x + 2.25) equal to 12.691040146 and -12.691040146.Subproblem 1
x + 2.25 = 12.691040146 Simplifying x + 2.25 = 12.691040146 Reorder the terms: 2.25 + x = 12.691040146 Solving 2.25 + x = 12.691040146 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 = 12.691040146 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 12.691040146 + -2.25 x = 12.691040146 + -2.25 Combine like terms: 12.691040146 + -2.25 = 10.441040146 x = 10.441040146 Simplifying x = 10.441040146Subproblem 2
x + 2.25 = -12.691040146 Simplifying x + 2.25 = -12.691040146 Reorder the terms: 2.25 + x = -12.691040146 Solving 2.25 + x = -12.691040146 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 = -12.691040146 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -12.691040146 + -2.25 x = -12.691040146 + -2.25 Combine like terms: -12.691040146 + -2.25 = -14.941040146 x = -14.941040146 Simplifying x = -14.941040146Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.441040146, -14.941040146}
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