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Simplifying 2x2 + -9x = 222 Reorder the terms: -9x + 2x2 = 222 Solving -9x + 2x2 = 222 Solving for variable 'x'. Reorder the terms: -222 + -9x + 2x2 = 222 + -222 Combine like terms: 222 + -222 = 0 -222 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -111 + -4.5x + x2 = 0 Move the constant term to the right: Add '111' to each side of the equation. -111 + -4.5x + 111 + x2 = 0 + 111 Reorder the terms: -111 + 111 + -4.5x + x2 = 0 + 111 Combine like terms: -111 + 111 = 0 0 + -4.5x + x2 = 0 + 111 -4.5x + x2 = 0 + 111 Combine like terms: 0 + 111 = 111 -4.5x + x2 = 111 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 = 111 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 111 + 5.0625 Combine like terms: 111 + 5.0625 = 116.0625 5.0625 + -4.5x + x2 = 116.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 116.0625 Calculate the square root of the right side: 10.773230713 Break this problem into two subproblems by setting (x + -2.25) equal to 10.773230713 and -10.773230713.Subproblem 1
x + -2.25 = 10.773230713 Simplifying x + -2.25 = 10.773230713 Reorder the terms: -2.25 + x = 10.773230713 Solving -2.25 + x = 10.773230713 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 = 10.773230713 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 10.773230713 + 2.25 x = 10.773230713 + 2.25 Combine like terms: 10.773230713 + 2.25 = 13.023230713 x = 13.023230713 Simplifying x = 13.023230713Subproblem 2
x + -2.25 = -10.773230713 Simplifying x + -2.25 = -10.773230713 Reorder the terms: -2.25 + x = -10.773230713 Solving -2.25 + x = -10.773230713 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 = -10.773230713 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -10.773230713 + 2.25 x = -10.773230713 + 2.25 Combine like terms: -10.773230713 + 2.25 = -8.523230713 x = -8.523230713 Simplifying x = -8.523230713Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.023230713, -8.523230713}
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