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Simplifying 25x2 + -230x + 4 = 0 Reorder the terms: 4 + -230x + 25x2 = 0 Solving 4 + -230x + 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'. 0.16 + -9.2x + x2 = 0 Move the constant term to the right: Add '-0.16' to each side of the equation. 0.16 + -9.2x + -0.16 + x2 = 0 + -0.16 Reorder the terms: 0.16 + -0.16 + -9.2x + x2 = 0 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + -9.2x + x2 = 0 + -0.16 -9.2x + x2 = 0 + -0.16 Combine like terms: 0 + -0.16 = -0.16 -9.2x + x2 = -0.16 The x term is -9.2x. Take half its coefficient (-4.6). Square it (21.16) and add it to both sides. Add '21.16' to each side of the equation. -9.2x + 21.16 + x2 = -0.16 + 21.16 Reorder the terms: 21.16 + -9.2x + x2 = -0.16 + 21.16 Combine like terms: -0.16 + 21.16 = 21 21.16 + -9.2x + x2 = 21 Factor a perfect square on the left side: (x + -4.6)(x + -4.6) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + -4.6) equal to 4.582575695 and -4.582575695.Subproblem 1
x + -4.6 = 4.582575695 Simplifying x + -4.6 = 4.582575695 Reorder the terms: -4.6 + x = 4.582575695 Solving -4.6 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6' to each side of the equation. -4.6 + 4.6 + x = 4.582575695 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + x = 4.582575695 + 4.6 x = 4.582575695 + 4.6 Combine like terms: 4.582575695 + 4.6 = 9.182575695 x = 9.182575695 Simplifying x = 9.182575695Subproblem 2
x + -4.6 = -4.582575695 Simplifying x + -4.6 = -4.582575695 Reorder the terms: -4.6 + x = -4.582575695 Solving -4.6 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.6' to each side of the equation. -4.6 + 4.6 + x = -4.582575695 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + x = -4.582575695 + 4.6 x = -4.582575695 + 4.6 Combine like terms: -4.582575695 + 4.6 = 0.017424305 x = 0.017424305 Simplifying x = 0.017424305Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.182575695, 0.017424305}
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