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Simplifying 2x2 + -9x = 400 Reorder the terms: -9x + 2x2 = 400 Solving -9x + 2x2 = 400 Solving for variable 'x'. Reorder the terms: -400 + -9x + 2x2 = 400 + -400 Combine like terms: 400 + -400 = 0 -400 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -200 + -4.5x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -4.5x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -4.5x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -4.5x + x2 = 0 + 200 -4.5x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -4.5x + x2 = 200 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 = 200 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 200 + 5.0625 Combine like terms: 200 + 5.0625 = 205.0625 5.0625 + -4.5x + x2 = 205.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 205.0625 Calculate the square root of the right side: 14.320003492 Break this problem into two subproblems by setting (x + -2.25) equal to 14.320003492 and -14.320003492.Subproblem 1
x + -2.25 = 14.320003492 Simplifying x + -2.25 = 14.320003492 Reorder the terms: -2.25 + x = 14.320003492 Solving -2.25 + x = 14.320003492 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 = 14.320003492 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 14.320003492 + 2.25 x = 14.320003492 + 2.25 Combine like terms: 14.320003492 + 2.25 = 16.570003492 x = 16.570003492 Simplifying x = 16.570003492Subproblem 2
x + -2.25 = -14.320003492 Simplifying x + -2.25 = -14.320003492 Reorder the terms: -2.25 + x = -14.320003492 Solving -2.25 + x = -14.320003492 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 = -14.320003492 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -14.320003492 + 2.25 x = -14.320003492 + 2.25 Combine like terms: -14.320003492 + 2.25 = -12.070003492 x = -12.070003492 Simplifying x = -12.070003492Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.570003492, -12.070003492}
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