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Simplifying 16x2 + 96x + 141 = 0 Reorder the terms: 141 + 96x + 16x2 = 0 Solving 141 + 96x + 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'. 8.8125 + 6x + x2 = 0 Move the constant term to the right: Add '-8.8125' to each side of the equation. 8.8125 + 6x + -8.8125 + x2 = 0 + -8.8125 Reorder the terms: 8.8125 + -8.8125 + 6x + x2 = 0 + -8.8125 Combine like terms: 8.8125 + -8.8125 = 0.0000 0.0000 + 6x + x2 = 0 + -8.8125 6x + x2 = 0 + -8.8125 Combine like terms: 0 + -8.8125 = -8.8125 6x + x2 = -8.8125 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 = -8.8125 + 9 Reorder the terms: 9 + 6x + x2 = -8.8125 + 9 Combine like terms: -8.8125 + 9 = 0.1875 9 + 6x + x2 = 0.1875 Factor a perfect square on the left side: (x + 3)(x + 3) = 0.1875 Calculate the square root of the right side: 0.433012702 Break this problem into two subproblems by setting (x + 3) equal to 0.433012702 and -0.433012702.Subproblem 1
x + 3 = 0.433012702 Simplifying x + 3 = 0.433012702 Reorder the terms: 3 + x = 0.433012702 Solving 3 + x = 0.433012702 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 = 0.433012702 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0.433012702 + -3 x = 0.433012702 + -3 Combine like terms: 0.433012702 + -3 = -2.566987298 x = -2.566987298 Simplifying x = -2.566987298Subproblem 2
x + 3 = -0.433012702 Simplifying x + 3 = -0.433012702 Reorder the terms: 3 + x = -0.433012702 Solving 3 + x = -0.433012702 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 = -0.433012702 + -3 Combine like terms: 3 + -3 = 0 0 + x = -0.433012702 + -3 x = -0.433012702 + -3 Combine like terms: -0.433012702 + -3 = -3.433012702 x = -3.433012702 Simplifying x = -3.433012702Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.566987298, -3.433012702}
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