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Simplifying 25x2 + -254x + 247 = 0 Reorder the terms: 247 + -254x + 25x2 = 0 Solving 247 + -254x + 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'. 9.88 + -10.16x + x2 = 0 Move the constant term to the right: Add '-9.88' to each side of the equation. 9.88 + -10.16x + -9.88 + x2 = 0 + -9.88 Reorder the terms: 9.88 + -9.88 + -10.16x + x2 = 0 + -9.88 Combine like terms: 9.88 + -9.88 = 0.00 0.00 + -10.16x + x2 = 0 + -9.88 -10.16x + x2 = 0 + -9.88 Combine like terms: 0 + -9.88 = -9.88 -10.16x + x2 = -9.88 The x term is -10.16x. Take half its coefficient (-5.08). Square it (25.8064) and add it to both sides. Add '25.8064' to each side of the equation. -10.16x + 25.8064 + x2 = -9.88 + 25.8064 Reorder the terms: 25.8064 + -10.16x + x2 = -9.88 + 25.8064 Combine like terms: -9.88 + 25.8064 = 15.9264 25.8064 + -10.16x + x2 = 15.9264 Factor a perfect square on the left side: (x + -5.08)(x + -5.08) = 15.9264 Calculate the square root of the right side: 3.990789396 Break this problem into two subproblems by setting (x + -5.08) equal to 3.990789396 and -3.990789396.Subproblem 1
x + -5.08 = 3.990789396 Simplifying x + -5.08 = 3.990789396 Reorder the terms: -5.08 + x = 3.990789396 Solving -5.08 + x = 3.990789396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.08' to each side of the equation. -5.08 + 5.08 + x = 3.990789396 + 5.08 Combine like terms: -5.08 + 5.08 = 0.00 0.00 + x = 3.990789396 + 5.08 x = 3.990789396 + 5.08 Combine like terms: 3.990789396 + 5.08 = 9.070789396 x = 9.070789396 Simplifying x = 9.070789396Subproblem 2
x + -5.08 = -3.990789396 Simplifying x + -5.08 = -3.990789396 Reorder the terms: -5.08 + x = -3.990789396 Solving -5.08 + x = -3.990789396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.08' to each side of the equation. -5.08 + 5.08 + x = -3.990789396 + 5.08 Combine like terms: -5.08 + 5.08 = 0.00 0.00 + x = -3.990789396 + 5.08 x = -3.990789396 + 5.08 Combine like terms: -3.990789396 + 5.08 = 1.089210604 x = 1.089210604 Simplifying x = 1.089210604Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.070789396, 1.089210604}
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