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Simplifying (x2 + 9x + -2) + -1(9x2 + -4x + -4) = 0 Reorder the terms: (-2 + 9x + x2) + -1(9x2 + -4x + -4) = 0 Remove parenthesis around (-2 + 9x + x2) -2 + 9x + x2 + -1(9x2 + -4x + -4) = 0 Reorder the terms: -2 + 9x + x2 + -1(-4 + -4x + 9x2) = 0 -2 + 9x + x2 + (-4 * -1 + -4x * -1 + 9x2 * -1) = 0 -2 + 9x + x2 + (4 + 4x + -9x2) = 0 Reorder the terms: -2 + 4 + 9x + 4x + x2 + -9x2 = 0 Combine like terms: -2 + 4 = 2 2 + 9x + 4x + x2 + -9x2 = 0 Combine like terms: 9x + 4x = 13x 2 + 13x + x2 + -9x2 = 0 Combine like terms: x2 + -9x2 = -8x2 2 + 13x + -8x2 = 0 Solving 2 + 13x + -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'. -0.25 + -1.625x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.625x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.625x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.625x + x2 = 0 + 0.25 -1.625x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.625x + x2 = 0.25 The x term is -1.625x. Take half its coefficient (-0.8125). Square it (0.66015625) and add it to both sides. Add '0.66015625' to each side of the equation. -1.625x + 0.66015625 + x2 = 0.25 + 0.66015625 Reorder the terms: 0.66015625 + -1.625x + x2 = 0.25 + 0.66015625 Combine like terms: 0.25 + 0.66015625 = 0.91015625 0.66015625 + -1.625x + x2 = 0.91015625 Factor a perfect square on the left side: (x + -0.8125)(x + -0.8125) = 0.91015625 Calculate the square root of the right side: 0.954021095 Break this problem into two subproblems by setting (x + -0.8125) equal to 0.954021095 and -0.954021095.Subproblem 1
x + -0.8125 = 0.954021095 Simplifying x + -0.8125 = 0.954021095 Reorder the terms: -0.8125 + x = 0.954021095 Solving -0.8125 + x = 0.954021095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = 0.954021095 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = 0.954021095 + 0.8125 x = 0.954021095 + 0.8125 Combine like terms: 0.954021095 + 0.8125 = 1.766521095 x = 1.766521095 Simplifying x = 1.766521095Subproblem 2
x + -0.8125 = -0.954021095 Simplifying x + -0.8125 = -0.954021095 Reorder the terms: -0.8125 + x = -0.954021095 Solving -0.8125 + x = -0.954021095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8125' to each side of the equation. -0.8125 + 0.8125 + x = -0.954021095 + 0.8125 Combine like terms: -0.8125 + 0.8125 = 0.0000 0.0000 + x = -0.954021095 + 0.8125 x = -0.954021095 + 0.8125 Combine like terms: -0.954021095 + 0.8125 = -0.141521095 x = -0.141521095 Simplifying x = -0.141521095Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.766521095, -0.141521095}
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