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Simplifying 32x2 + -192x = 11 Reorder the terms: -192x + 32x2 = 11 Solving -192x + 32x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -192x + 32x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -192x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.34375 + -6x + x2 = 0 Move the constant term to the right: Add '0.34375' to each side of the equation. -0.34375 + -6x + 0.34375 + x2 = 0 + 0.34375 Reorder the terms: -0.34375 + 0.34375 + -6x + x2 = 0 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + -6x + x2 = 0 + 0.34375 -6x + x2 = 0 + 0.34375 Combine like terms: 0 + 0.34375 = 0.34375 -6x + x2 = 0.34375 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 0.34375 + 9 Reorder the terms: 9 + -6x + x2 = 0.34375 + 9 Combine like terms: 0.34375 + 9 = 9.34375 9 + -6x + x2 = 9.34375 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.34375 Calculate the square root of the right side: 3.056754815 Break this problem into two subproblems by setting (x + -3) equal to 3.056754815 and -3.056754815.Subproblem 1
x + -3 = 3.056754815 Simplifying x + -3 = 3.056754815 Reorder the terms: -3 + x = 3.056754815 Solving -3 + x = 3.056754815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.056754815 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.056754815 + 3 x = 3.056754815 + 3 Combine like terms: 3.056754815 + 3 = 6.056754815 x = 6.056754815 Simplifying x = 6.056754815Subproblem 2
x + -3 = -3.056754815 Simplifying x + -3 = -3.056754815 Reorder the terms: -3 + x = -3.056754815 Solving -3 + x = -3.056754815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.056754815 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.056754815 + 3 x = -3.056754815 + 3 Combine like terms: -3.056754815 + 3 = -0.056754815 x = -0.056754815 Simplifying x = -0.056754815Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.056754815, -0.056754815}
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