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Simplifying 25x2 + -236x + -644 = 0 Reorder the terms: -644 + -236x + 25x2 = 0 Solving -644 + -236x + 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'. -25.76 + -9.44x + x2 = 0 Move the constant term to the right: Add '25.76' to each side of the equation. -25.76 + -9.44x + 25.76 + x2 = 0 + 25.76 Reorder the terms: -25.76 + 25.76 + -9.44x + x2 = 0 + 25.76 Combine like terms: -25.76 + 25.76 = 0.00 0.00 + -9.44x + x2 = 0 + 25.76 -9.44x + x2 = 0 + 25.76 Combine like terms: 0 + 25.76 = 25.76 -9.44x + x2 = 25.76 The x term is -9.44x. Take half its coefficient (-4.72). Square it (22.2784) and add it to both sides. Add '22.2784' to each side of the equation. -9.44x + 22.2784 + x2 = 25.76 + 22.2784 Reorder the terms: 22.2784 + -9.44x + x2 = 25.76 + 22.2784 Combine like terms: 25.76 + 22.2784 = 48.0384 22.2784 + -9.44x + x2 = 48.0384 Factor a perfect square on the left side: (x + -4.72)(x + -4.72) = 48.0384 Calculate the square root of the right side: 6.930973958 Break this problem into two subproblems by setting (x + -4.72) equal to 6.930973958 and -6.930973958.Subproblem 1
x + -4.72 = 6.930973958 Simplifying x + -4.72 = 6.930973958 Reorder the terms: -4.72 + x = 6.930973958 Solving -4.72 + x = 6.930973958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.72' to each side of the equation. -4.72 + 4.72 + x = 6.930973958 + 4.72 Combine like terms: -4.72 + 4.72 = 0.00 0.00 + x = 6.930973958 + 4.72 x = 6.930973958 + 4.72 Combine like terms: 6.930973958 + 4.72 = 11.650973958 x = 11.650973958 Simplifying x = 11.650973958Subproblem 2
x + -4.72 = -6.930973958 Simplifying x + -4.72 = -6.930973958 Reorder the terms: -4.72 + x = -6.930973958 Solving -4.72 + x = -6.930973958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.72' to each side of the equation. -4.72 + 4.72 + x = -6.930973958 + 4.72 Combine like terms: -4.72 + 4.72 = 0.00 0.00 + x = -6.930973958 + 4.72 x = -6.930973958 + 4.72 Combine like terms: -6.930973958 + 4.72 = -2.210973958 x = -2.210973958 Simplifying x = -2.210973958Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.650973958, -2.210973958}
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