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Simplifying 5x2 + 10x + -96 = 0 Reorder the terms: -96 + 10x + 5x2 = 0 Solving -96 + 10x + 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'. -19.2 + 2x + x2 = 0 Move the constant term to the right: Add '19.2' to each side of the equation. -19.2 + 2x + 19.2 + x2 = 0 + 19.2 Reorder the terms: -19.2 + 19.2 + 2x + x2 = 0 + 19.2 Combine like terms: -19.2 + 19.2 = 0.0 0.0 + 2x + x2 = 0 + 19.2 2x + x2 = 0 + 19.2 Combine like terms: 0 + 19.2 = 19.2 2x + x2 = 19.2 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 19.2 + 1 Reorder the terms: 1 + 2x + x2 = 19.2 + 1 Combine like terms: 19.2 + 1 = 20.2 1 + 2x + x2 = 20.2 Factor a perfect square on the left side: (x + 1)(x + 1) = 20.2 Calculate the square root of the right side: 4.494441011 Break this problem into two subproblems by setting (x + 1) equal to 4.494441011 and -4.494441011.Subproblem 1
x + 1 = 4.494441011 Simplifying x + 1 = 4.494441011 Reorder the terms: 1 + x = 4.494441011 Solving 1 + x = 4.494441011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.494441011 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.494441011 + -1 x = 4.494441011 + -1 Combine like terms: 4.494441011 + -1 = 3.494441011 x = 3.494441011 Simplifying x = 3.494441011Subproblem 2
x + 1 = -4.494441011 Simplifying x + 1 = -4.494441011 Reorder the terms: 1 + x = -4.494441011 Solving 1 + x = -4.494441011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.494441011 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.494441011 + -1 x = -4.494441011 + -1 Combine like terms: -4.494441011 + -1 = -5.494441011 x = -5.494441011 Simplifying x = -5.494441011Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.494441011, -5.494441011}
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