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Simplifying 11x2 + 6 + -8x + -3x2 + -13x = 0 Reorder the terms: 6 + -8x + -13x + 11x2 + -3x2 = 0 Combine like terms: -8x + -13x = -21x 6 + -21x + 11x2 + -3x2 = 0 Combine like terms: 11x2 + -3x2 = 8x2 6 + -21x + 8x2 = 0 Solving 6 + -21x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.75 + -2.625x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -2.625x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -2.625x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -2.625x + x2 = 0 + -0.75 -2.625x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -2.625x + x2 = -0.75 The x term is -2.625x. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625x + 1.72265625 + x2 = -0.75 + 1.72265625 Reorder the terms: 1.72265625 + -2.625x + x2 = -0.75 + 1.72265625 Combine like terms: -0.75 + 1.72265625 = 0.97265625 1.72265625 + -2.625x + x2 = 0.97265625 Factor a perfect square on the left side: (x + -1.3125)(x + -1.3125) = 0.97265625 Calculate the square root of the right side: 0.986233365 Break this problem into two subproblems by setting (x + -1.3125) equal to 0.986233365 and -0.986233365.Subproblem 1
x + -1.3125 = 0.986233365 Simplifying x + -1.3125 = 0.986233365 Reorder the terms: -1.3125 + x = 0.986233365 Solving -1.3125 + x = 0.986233365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = 0.986233365 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = 0.986233365 + 1.3125 x = 0.986233365 + 1.3125 Combine like terms: 0.986233365 + 1.3125 = 2.298733365 x = 2.298733365 Simplifying x = 2.298733365Subproblem 2
x + -1.3125 = -0.986233365 Simplifying x + -1.3125 = -0.986233365 Reorder the terms: -1.3125 + x = -0.986233365 Solving -1.3125 + x = -0.986233365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = -0.986233365 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = -0.986233365 + 1.3125 x = -0.986233365 + 1.3125 Combine like terms: -0.986233365 + 1.3125 = 0.326266635 x = 0.326266635 Simplifying x = 0.326266635Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.298733365, 0.326266635}
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