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Simplifying -3x2 + -2 + 5x + 11x2 + -14x = 0 Reorder the terms: -2 + 5x + -14x + -3x2 + 11x2 = 0 Combine like terms: 5x + -14x = -9x -2 + -9x + -3x2 + 11x2 = 0 Combine like terms: -3x2 + 11x2 = 8x2 -2 + -9x + 8x2 = 0 Solving -2 + -9x + 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 + -1.125x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1.125x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1.125x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1.125x + x2 = 0 + 0.25 -1.125x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1.125x + x2 = 0.25 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = 0.25 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 0.25 + 0.31640625 Combine like terms: 0.25 + 0.31640625 = 0.56640625 0.31640625 + -1.125x + x2 = 0.56640625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 0.56640625 Calculate the square root of the right side: 0.752599661 Break this problem into two subproblems by setting (x + -0.5625) equal to 0.752599661 and -0.752599661.Subproblem 1
x + -0.5625 = 0.752599661 Simplifying x + -0.5625 = 0.752599661 Reorder the terms: -0.5625 + x = 0.752599661 Solving -0.5625 + x = 0.752599661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 0.752599661 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 0.752599661 + 0.5625 x = 0.752599661 + 0.5625 Combine like terms: 0.752599661 + 0.5625 = 1.315099661 x = 1.315099661 Simplifying x = 1.315099661Subproblem 2
x + -0.5625 = -0.752599661 Simplifying x + -0.5625 = -0.752599661 Reorder the terms: -0.5625 + x = -0.752599661 Solving -0.5625 + x = -0.752599661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -0.752599661 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -0.752599661 + 0.5625 x = -0.752599661 + 0.5625 Combine like terms: -0.752599661 + 0.5625 = -0.190099661 x = -0.190099661 Simplifying x = -0.190099661Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.315099661, -0.190099661}
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