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Simplifying 2x2 + 9x2 + -50x + -225 = 0 Reorder the terms: -225 + -50x + 2x2 + 9x2 = 0 Combine like terms: 2x2 + 9x2 = 11x2 -225 + -50x + 11x2 = 0 Solving -225 + -50x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -20.45454545 + -4.545454545x + x2 = 0 Move the constant term to the right: Add '20.45454545' to each side of the equation. -20.45454545 + -4.545454545x + 20.45454545 + x2 = 0 + 20.45454545 Reorder the terms: -20.45454545 + 20.45454545 + -4.545454545x + x2 = 0 + 20.45454545 Combine like terms: -20.45454545 + 20.45454545 = 0.00000000 0.00000000 + -4.545454545x + x2 = 0 + 20.45454545 -4.545454545x + x2 = 0 + 20.45454545 Combine like terms: 0 + 20.45454545 = 20.45454545 -4.545454545x + x2 = 20.45454545 The x term is -4.545454545x. Take half its coefficient (-2.272727273). Square it (5.165289257) and add it to both sides. Add '5.165289257' to each side of the equation. -4.545454545x + 5.165289257 + x2 = 20.45454545 + 5.165289257 Reorder the terms: 5.165289257 + -4.545454545x + x2 = 20.45454545 + 5.165289257 Combine like terms: 20.45454545 + 5.165289257 = 25.619834707 5.165289257 + -4.545454545x + x2 = 25.619834707 Factor a perfect square on the left side: (x + -2.272727273)(x + -2.272727273) = 25.619834707 Calculate the square root of the right side: 5.061603966 Break this problem into two subproblems by setting (x + -2.272727273) equal to 5.061603966 and -5.061603966.Subproblem 1
x + -2.272727273 = 5.061603966 Simplifying x + -2.272727273 = 5.061603966 Reorder the terms: -2.272727273 + x = 5.061603966 Solving -2.272727273 + x = 5.061603966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.272727273' to each side of the equation. -2.272727273 + 2.272727273 + x = 5.061603966 + 2.272727273 Combine like terms: -2.272727273 + 2.272727273 = 0.000000000 0.000000000 + x = 5.061603966 + 2.272727273 x = 5.061603966 + 2.272727273 Combine like terms: 5.061603966 + 2.272727273 = 7.334331239 x = 7.334331239 Simplifying x = 7.334331239Subproblem 2
x + -2.272727273 = -5.061603966 Simplifying x + -2.272727273 = -5.061603966 Reorder the terms: -2.272727273 + x = -5.061603966 Solving -2.272727273 + x = -5.061603966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.272727273' to each side of the equation. -2.272727273 + 2.272727273 + x = -5.061603966 + 2.272727273 Combine like terms: -2.272727273 + 2.272727273 = 0.000000000 0.000000000 + x = -5.061603966 + 2.272727273 x = -5.061603966 + 2.272727273 Combine like terms: -5.061603966 + 2.272727273 = -2.788876693 x = -2.788876693 Simplifying x = -2.788876693Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.334331239, -2.788876693}
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