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Simplifying 5x2 + -16x + -384 = 0 Reorder the terms: -384 + -16x + 5x2 = 0 Solving -384 + -16x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -76.8 + -3.2x + x2 = 0 Move the constant term to the right: Add '76.8' to each side of the equation. -76.8 + -3.2x + 76.8 + x2 = 0 + 76.8 Reorder the terms: -76.8 + 76.8 + -3.2x + x2 = 0 + 76.8 Combine like terms: -76.8 + 76.8 = 0.0 0.0 + -3.2x + x2 = 0 + 76.8 -3.2x + x2 = 0 + 76.8 Combine like terms: 0 + 76.8 = 76.8 -3.2x + x2 = 76.8 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 76.8 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 76.8 + 2.56 Combine like terms: 76.8 + 2.56 = 79.36 2.56 + -3.2x + x2 = 79.36 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 79.36 Calculate the square root of the right side: 8.908422981 Break this problem into two subproblems by setting (x + -1.6) equal to 8.908422981 and -8.908422981.Subproblem 1
x + -1.6 = 8.908422981 Simplifying x + -1.6 = 8.908422981 Reorder the terms: -1.6 + x = 8.908422981 Solving -1.6 + x = 8.908422981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 8.908422981 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 8.908422981 + 1.6 x = 8.908422981 + 1.6 Combine like terms: 8.908422981 + 1.6 = 10.508422981 x = 10.508422981 Simplifying x = 10.508422981Subproblem 2
x + -1.6 = -8.908422981 Simplifying x + -1.6 = -8.908422981 Reorder the terms: -1.6 + x = -8.908422981 Solving -1.6 + x = -8.908422981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -8.908422981 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -8.908422981 + 1.6 x = -8.908422981 + 1.6 Combine like terms: -8.908422981 + 1.6 = -7.308422981 x = -7.308422981 Simplifying x = -7.308422981Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.508422981, -7.308422981}
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