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Simplifying 25x2 + -230x + 46 = 0 Reorder the terms: 46 + -230x + 25x2 = 0 Solving 46 + -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'. 1.84 + -9.2x + x2 = 0 Move the constant term to the right: Add '-1.84' to each side of the equation. 1.84 + -9.2x + -1.84 + x2 = 0 + -1.84 Reorder the terms: 1.84 + -1.84 + -9.2x + x2 = 0 + -1.84 Combine like terms: 1.84 + -1.84 = 0.00 0.00 + -9.2x + x2 = 0 + -1.84 -9.2x + x2 = 0 + -1.84 Combine like terms: 0 + -1.84 = -1.84 -9.2x + x2 = -1.84 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 = -1.84 + 21.16 Reorder the terms: 21.16 + -9.2x + x2 = -1.84 + 21.16 Combine like terms: -1.84 + 21.16 = 19.32 21.16 + -9.2x + x2 = 19.32 Factor a perfect square on the left side: (x + -4.6)(x + -4.6) = 19.32 Calculate the square root of the right side: 4.395452195 Break this problem into two subproblems by setting (x + -4.6) equal to 4.395452195 and -4.395452195.Subproblem 1
x + -4.6 = 4.395452195 Simplifying x + -4.6 = 4.395452195 Reorder the terms: -4.6 + x = 4.395452195 Solving -4.6 + x = 4.395452195 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 = 4.395452195 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + x = 4.395452195 + 4.6 x = 4.395452195 + 4.6 Combine like terms: 4.395452195 + 4.6 = 8.995452195 x = 8.995452195 Simplifying x = 8.995452195Subproblem 2
x + -4.6 = -4.395452195 Simplifying x + -4.6 = -4.395452195 Reorder the terms: -4.6 + x = -4.395452195 Solving -4.6 + x = -4.395452195 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 = -4.395452195 + 4.6 Combine like terms: -4.6 + 4.6 = 0.0 0.0 + x = -4.395452195 + 4.6 x = -4.395452195 + 4.6 Combine like terms: -4.395452195 + 4.6 = 0.204547805 x = 0.204547805 Simplifying x = 0.204547805Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.995452195, 0.204547805}
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