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Simplifying 125x + -16x2 + 6 = 0 Reorder the terms: 6 + 125x + -16x2 = 0 Solving 6 + 125x + -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'. -0.375 + -7.8125x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -7.8125x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -7.8125x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -7.8125x + x2 = 0 + 0.375 -7.8125x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -7.8125x + x2 = 0.375 The x term is -7.8125x. Take half its coefficient (-3.90625). Square it (15.25878906) and add it to both sides. Add '15.25878906' to each side of the equation. -7.8125x + 15.25878906 + x2 = 0.375 + 15.25878906 Reorder the terms: 15.25878906 + -7.8125x + x2 = 0.375 + 15.25878906 Combine like terms: 0.375 + 15.25878906 = 15.63378906 15.25878906 + -7.8125x + x2 = 15.63378906 Factor a perfect square on the left side: (x + -3.90625)(x + -3.90625) = 15.63378906 Calculate the square root of the right side: 3.953958657 Break this problem into two subproblems by setting (x + -3.90625) equal to 3.953958657 and -3.953958657.Subproblem 1
x + -3.90625 = 3.953958657 Simplifying x + -3.90625 = 3.953958657 Reorder the terms: -3.90625 + x = 3.953958657 Solving -3.90625 + x = 3.953958657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.90625' to each side of the equation. -3.90625 + 3.90625 + x = 3.953958657 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + x = 3.953958657 + 3.90625 x = 3.953958657 + 3.90625 Combine like terms: 3.953958657 + 3.90625 = 7.860208657 x = 7.860208657 Simplifying x = 7.860208657Subproblem 2
x + -3.90625 = -3.953958657 Simplifying x + -3.90625 = -3.953958657 Reorder the terms: -3.90625 + x = -3.953958657 Solving -3.90625 + x = -3.953958657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.90625' to each side of the equation. -3.90625 + 3.90625 + x = -3.953958657 + 3.90625 Combine like terms: -3.90625 + 3.90625 = 0.00000 0.00000 + x = -3.953958657 + 3.90625 x = -3.953958657 + 3.90625 Combine like terms: -3.953958657 + 3.90625 = -0.047708657 x = -0.047708657 Simplifying x = -0.047708657Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.860208657, -0.047708657}
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