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Simplifying 25x2 + 40x + -68 = 0 Reorder the terms: -68 + 40x + 25x2 = 0 Solving -68 + 40x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.72 + 1.6x + x2 = 0 Move the constant term to the right: Add '2.72' to each side of the equation. -2.72 + 1.6x + 2.72 + x2 = 0 + 2.72 Reorder the terms: -2.72 + 2.72 + 1.6x + x2 = 0 + 2.72 Combine like terms: -2.72 + 2.72 = 0.00 0.00 + 1.6x + x2 = 0 + 2.72 1.6x + x2 = 0 + 2.72 Combine like terms: 0 + 2.72 = 2.72 1.6x + x2 = 2.72 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 2.72 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 2.72 + 0.64 Combine like terms: 2.72 + 0.64 = 3.36 0.64 + 1.6x + x2 = 3.36 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 3.36 Calculate the square root of the right side: 1.833030278 Break this problem into two subproblems by setting (x + 0.8) equal to 1.833030278 and -1.833030278.Subproblem 1
x + 0.8 = 1.833030278 Simplifying x + 0.8 = 1.833030278 Reorder the terms: 0.8 + x = 1.833030278 Solving 0.8 + x = 1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 1.833030278 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.833030278 + -0.8 x = 1.833030278 + -0.8 Combine like terms: 1.833030278 + -0.8 = 1.033030278 x = 1.033030278 Simplifying x = 1.033030278Subproblem 2
x + 0.8 = -1.833030278 Simplifying x + 0.8 = -1.833030278 Reorder the terms: 0.8 + x = -1.833030278 Solving 0.8 + x = -1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -1.833030278 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.833030278 + -0.8 x = -1.833030278 + -0.8 Combine like terms: -1.833030278 + -0.8 = -2.633030278 x = -2.633030278 Simplifying x = -2.633030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.033030278, -2.633030278}
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