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Simplifying 5x2 + 16x + -3584 = 0 Reorder the terms: -3584 + 16x + 5x2 = 0 Solving -3584 + 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'. -716.8 + 3.2x + x2 = 0 Move the constant term to the right: Add '716.8' to each side of the equation. -716.8 + 3.2x + 716.8 + x2 = 0 + 716.8 Reorder the terms: -716.8 + 716.8 + 3.2x + x2 = 0 + 716.8 Combine like terms: -716.8 + 716.8 = 0.0 0.0 + 3.2x + x2 = 0 + 716.8 3.2x + x2 = 0 + 716.8 Combine like terms: 0 + 716.8 = 716.8 3.2x + x2 = 716.8 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 = 716.8 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = 716.8 + 2.56 Combine like terms: 716.8 + 2.56 = 719.36 2.56 + 3.2x + x2 = 719.36 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 719.36 Calculate the square root of the right side: 26.820887383 Break this problem into two subproblems by setting (x + 1.6) equal to 26.820887383 and -26.820887383.Subproblem 1
x + 1.6 = 26.820887383 Simplifying x + 1.6 = 26.820887383 Reorder the terms: 1.6 + x = 26.820887383 Solving 1.6 + x = 26.820887383 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 = 26.820887383 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 26.820887383 + -1.6 x = 26.820887383 + -1.6 Combine like terms: 26.820887383 + -1.6 = 25.220887383 x = 25.220887383 Simplifying x = 25.220887383Subproblem 2
x + 1.6 = -26.820887383 Simplifying x + 1.6 = -26.820887383 Reorder the terms: 1.6 + x = -26.820887383 Solving 1.6 + x = -26.820887383 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 = -26.820887383 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -26.820887383 + -1.6 x = -26.820887383 + -1.6 Combine like terms: -26.820887383 + -1.6 = -28.420887383 x = -28.420887383 Simplifying x = -28.420887383Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.220887383, -28.420887383}
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