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Simplifying 16x2 + -24x + -11 = 0 Reorder the terms: -11 + -24x + 16x2 = 0 Solving -11 + -24x + 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'. -0.6875 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.6875' to each side of the equation. -0.6875 + -1.5x + 0.6875 + x2 = 0 + 0.6875 Reorder the terms: -0.6875 + 0.6875 + -1.5x + x2 = 0 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + -1.5x + x2 = 0 + 0.6875 -1.5x + x2 = 0 + 0.6875 Combine like terms: 0 + 0.6875 = 0.6875 -1.5x + x2 = 0.6875 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.6875 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.6875 + 0.5625 Combine like terms: 0.6875 + 0.5625 = 1.25 0.5625 + -1.5x + x2 = 1.25 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -0.75) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -0.75 = 1.118033989 Simplifying x + -0.75 = 1.118033989 Reorder the terms: -0.75 + x = 1.118033989 Solving -0.75 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.118033989 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.118033989 + 0.75 x = 1.118033989 + 0.75 Combine like terms: 1.118033989 + 0.75 = 1.868033989 x = 1.868033989 Simplifying x = 1.868033989Subproblem 2
x + -0.75 = -1.118033989 Simplifying x + -0.75 = -1.118033989 Reorder the terms: -0.75 + x = -1.118033989 Solving -0.75 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.118033989 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.118033989 + 0.75 x = -1.118033989 + 0.75 Combine like terms: -1.118033989 + 0.75 = -0.368033989 x = -0.368033989 Simplifying x = -0.368033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.868033989, -0.368033989}
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