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Simplifying 16x2 + 195x + -87 = 0 Reorder the terms: -87 + 195x + 16x2 = 0 Solving -87 + 195x + 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'. -5.4375 + 12.1875x + x2 = 0 Move the constant term to the right: Add '5.4375' to each side of the equation. -5.4375 + 12.1875x + 5.4375 + x2 = 0 + 5.4375 Reorder the terms: -5.4375 + 5.4375 + 12.1875x + x2 = 0 + 5.4375 Combine like terms: -5.4375 + 5.4375 = 0.0000 0.0000 + 12.1875x + x2 = 0 + 5.4375 12.1875x + x2 = 0 + 5.4375 Combine like terms: 0 + 5.4375 = 5.4375 12.1875x + x2 = 5.4375 The x term is 12.1875x. Take half its coefficient (6.09375). Square it (37.13378906) and add it to both sides. Add '37.13378906' to each side of the equation. 12.1875x + 37.13378906 + x2 = 5.4375 + 37.13378906 Reorder the terms: 37.13378906 + 12.1875x + x2 = 5.4375 + 37.13378906 Combine like terms: 5.4375 + 37.13378906 = 42.57128906 37.13378906 + 12.1875x + x2 = 42.57128906 Factor a perfect square on the left side: (x + 6.09375)(x + 6.09375) = 42.57128906 Calculate the square root of the right side: 6.524667736 Break this problem into two subproblems by setting (x + 6.09375) equal to 6.524667736 and -6.524667736.Subproblem 1
x + 6.09375 = 6.524667736 Simplifying x + 6.09375 = 6.524667736 Reorder the terms: 6.09375 + x = 6.524667736 Solving 6.09375 + x = 6.524667736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.09375' to each side of the equation. 6.09375 + -6.09375 + x = 6.524667736 + -6.09375 Combine like terms: 6.09375 + -6.09375 = 0.00000 0.00000 + x = 6.524667736 + -6.09375 x = 6.524667736 + -6.09375 Combine like terms: 6.524667736 + -6.09375 = 0.430917736 x = 0.430917736 Simplifying x = 0.430917736Subproblem 2
x + 6.09375 = -6.524667736 Simplifying x + 6.09375 = -6.524667736 Reorder the terms: 6.09375 + x = -6.524667736 Solving 6.09375 + x = -6.524667736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.09375' to each side of the equation. 6.09375 + -6.09375 + x = -6.524667736 + -6.09375 Combine like terms: 6.09375 + -6.09375 = 0.00000 0.00000 + x = -6.524667736 + -6.09375 x = -6.524667736 + -6.09375 Combine like terms: -6.524667736 + -6.09375 = -12.618417736 x = -12.618417736 Simplifying x = -12.618417736Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.430917736, -12.618417736}
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