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Simplifying (-11x2 + 6x + 6) + (-5x2 + 3x + 2) = 0 Reorder the terms: (6 + 6x + -11x2) + (-5x2 + 3x + 2) = 0 Remove parenthesis around (6 + 6x + -11x2) 6 + 6x + -11x2 + (-5x2 + 3x + 2) = 0 Reorder the terms: 6 + 6x + -11x2 + (2 + 3x + -5x2) = 0 Remove parenthesis around (2 + 3x + -5x2) 6 + 6x + -11x2 + 2 + 3x + -5x2 = 0 Reorder the terms: 6 + 2 + 6x + 3x + -11x2 + -5x2 = 0 Combine like terms: 6 + 2 = 8 8 + 6x + 3x + -11x2 + -5x2 = 0 Combine like terms: 6x + 3x = 9x 8 + 9x + -11x2 + -5x2 = 0 Combine like terms: -11x2 + -5x2 = -16x2 8 + 9x + -16x2 = 0 Solving 8 + 9x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.5 + -0.5625x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.5625x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.5625x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.5625x + x2 = 0 + 0.5 -0.5625x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.5625x + x2 = 0.5 The x term is -0.5625x. Take half its coefficient (-0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. -0.5625x + 0.0791015625 + x2 = 0.5 + 0.0791015625 Reorder the terms: 0.0791015625 + -0.5625x + x2 = 0.5 + 0.0791015625 Combine like terms: 0.5 + 0.0791015625 = 0.5791015625 0.0791015625 + -0.5625x + x2 = 0.5791015625 Factor a perfect square on the left side: (x + -0.28125)(x + -0.28125) = 0.5791015625 Calculate the square root of the right side: 0.760987229 Break this problem into two subproblems by setting (x + -0.28125) equal to 0.760987229 and -0.760987229.Subproblem 1
x + -0.28125 = 0.760987229 Simplifying x + -0.28125 = 0.760987229 Reorder the terms: -0.28125 + x = 0.760987229 Solving -0.28125 + x = 0.760987229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = 0.760987229 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = 0.760987229 + 0.28125 x = 0.760987229 + 0.28125 Combine like terms: 0.760987229 + 0.28125 = 1.042237229 x = 1.042237229 Simplifying x = 1.042237229Subproblem 2
x + -0.28125 = -0.760987229 Simplifying x + -0.28125 = -0.760987229 Reorder the terms: -0.28125 + x = -0.760987229 Solving -0.28125 + x = -0.760987229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = -0.760987229 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = -0.760987229 + 0.28125 x = -0.760987229 + 0.28125 Combine like terms: -0.760987229 + 0.28125 = -0.479737229 x = -0.479737229 Simplifying x = -0.479737229Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.042237229, -0.479737229}
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