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Simplifying x(11 + -2x) = 10 (11 * x + -2x * x) = 10 (11x + -2x2) = 10 Solving 11x + -2x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 11x + -2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 11x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 5 + -5.5x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -5.5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -5.5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5.5x + x2 = 0 + -5 -5.5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5.5x + x2 = -5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -5 + 7.5625 Combine like terms: -5 + 7.5625 = 2.5625 7.5625 + -5.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -2.75) equal to 1.600781059 and -1.600781059.Subproblem 1
x + -2.75 = 1.600781059 Simplifying x + -2.75 = 1.600781059 Reorder the terms: -2.75 + x = 1.600781059 Solving -2.75 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 1.600781059 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 1.600781059 + 2.75 x = 1.600781059 + 2.75 Combine like terms: 1.600781059 + 2.75 = 4.350781059 x = 4.350781059 Simplifying x = 4.350781059Subproblem 2
x + -2.75 = -1.600781059 Simplifying x + -2.75 = -1.600781059 Reorder the terms: -2.75 + x = -1.600781059 Solving -2.75 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -1.600781059 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -1.600781059 + 2.75 x = -1.600781059 + 2.75 Combine like terms: -1.600781059 + 2.75 = 1.149218941 x = 1.149218941 Simplifying x = 1.149218941Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.350781059, 1.149218941}
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