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Simplifying (6x2 + -2x + 11) + (2x2 + 5x + -47) = 0 Reorder the terms: (11 + -2x + 6x2) + (2x2 + 5x + -47) = 0 Remove parenthesis around (11 + -2x + 6x2) 11 + -2x + 6x2 + (2x2 + 5x + -47) = 0 Reorder the terms: 11 + -2x + 6x2 + (-47 + 5x + 2x2) = 0 Remove parenthesis around (-47 + 5x + 2x2) 11 + -2x + 6x2 + -47 + 5x + 2x2 = 0 Reorder the terms: 11 + -47 + -2x + 5x + 6x2 + 2x2 = 0 Combine like terms: 11 + -47 = -36 -36 + -2x + 5x + 6x2 + 2x2 = 0 Combine like terms: -2x + 5x = 3x -36 + 3x + 6x2 + 2x2 = 0 Combine like terms: 6x2 + 2x2 = 8x2 -36 + 3x + 8x2 = 0 Solving -36 + 3x + 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'. -4.5 + 0.375x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 0.375x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 0.375x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 0.375x + x2 = 0 + 4.5 0.375x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 0.375x + x2 = 4.5 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 4.5 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 4.5 + 0.03515625 Combine like terms: 4.5 + 0.03515625 = 4.53515625 0.03515625 + 0.375x + x2 = 4.53515625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 4.53515625 Calculate the square root of the right side: 2.12959063 Break this problem into two subproblems by setting (x + 0.1875) equal to 2.12959063 and -2.12959063.Subproblem 1
x + 0.1875 = 2.12959063 Simplifying x + 0.1875 = 2.12959063 Reorder the terms: 0.1875 + x = 2.12959063 Solving 0.1875 + x = 2.12959063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 2.12959063 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 2.12959063 + -0.1875 x = 2.12959063 + -0.1875 Combine like terms: 2.12959063 + -0.1875 = 1.94209063 x = 1.94209063 Simplifying x = 1.94209063Subproblem 2
x + 0.1875 = -2.12959063 Simplifying x + 0.1875 = -2.12959063 Reorder the terms: 0.1875 + x = -2.12959063 Solving 0.1875 + x = -2.12959063 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -2.12959063 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -2.12959063 + -0.1875 x = -2.12959063 + -0.1875 Combine like terms: -2.12959063 + -0.1875 = -2.31709063 x = -2.31709063 Simplifying x = -2.31709063Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.94209063, -2.31709063}
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