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Simplifying (3x2 + -5x + -5) + (9x2 + 2x + 1) = 0 Reorder the terms: (-5 + -5x + 3x2) + (9x2 + 2x + 1) = 0 Remove parenthesis around (-5 + -5x + 3x2) -5 + -5x + 3x2 + (9x2 + 2x + 1) = 0 Reorder the terms: -5 + -5x + 3x2 + (1 + 2x + 9x2) = 0 Remove parenthesis around (1 + 2x + 9x2) -5 + -5x + 3x2 + 1 + 2x + 9x2 = 0 Reorder the terms: -5 + 1 + -5x + 2x + 3x2 + 9x2 = 0 Combine like terms: -5 + 1 = -4 -4 + -5x + 2x + 3x2 + 9x2 = 0 Combine like terms: -5x + 2x = -3x -4 + -3x + 3x2 + 9x2 = 0 Combine like terms: 3x2 + 9x2 = 12x2 -4 + -3x + 12x2 = 0 Solving -4 + -3x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.3333333333 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.25x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.25x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.25x + x2 = 0 + 0.3333333333 -0.25x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.25x + x2 = 0.3333333333 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.3333333333 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.3333333333 + 0.015625 Combine like terms: 0.3333333333 + 0.015625 = 0.3489583333 0.015625 + -0.25x + x2 = 0.3489583333 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.3489583333 Calculate the square root of the right side: 0.590726953 Break this problem into two subproblems by setting (x + -0.125) equal to 0.590726953 and -0.590726953.Subproblem 1
x + -0.125 = 0.590726953 Simplifying x + -0.125 = 0.590726953 Reorder the terms: -0.125 + x = 0.590726953 Solving -0.125 + x = 0.590726953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.590726953 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.590726953 + 0.125 x = 0.590726953 + 0.125 Combine like terms: 0.590726953 + 0.125 = 0.715726953 x = 0.715726953 Simplifying x = 0.715726953Subproblem 2
x + -0.125 = -0.590726953 Simplifying x + -0.125 = -0.590726953 Reorder the terms: -0.125 + x = -0.590726953 Solving -0.125 + x = -0.590726953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.590726953 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.590726953 + 0.125 x = -0.590726953 + 0.125 Combine like terms: -0.590726953 + 0.125 = -0.465726953 x = -0.465726953 Simplifying x = -0.465726953Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.715726953, -0.465726953}
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