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Simplifying 25x2 = 71 + -20x Solving 25x2 = 71 + -20x Solving for variable 'x'. Reorder the terms: -71 + 20x + 25x2 = 71 + -20x + -71 + 20x Reorder the terms: -71 + 20x + 25x2 = 71 + -71 + -20x + 20x Combine like terms: 71 + -71 = 0 -71 + 20x + 25x2 = 0 + -20x + 20x -71 + 20x + 25x2 = -20x + 20x Combine like terms: -20x + 20x = 0 -71 + 20x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.84 + 0.8x + x2 = 0 Move the constant term to the right: Add '2.84' to each side of the equation. -2.84 + 0.8x + 2.84 + x2 = 0 + 2.84 Reorder the terms: -2.84 + 2.84 + 0.8x + x2 = 0 + 2.84 Combine like terms: -2.84 + 2.84 = 0.00 0.00 + 0.8x + x2 = 0 + 2.84 0.8x + x2 = 0 + 2.84 Combine like terms: 0 + 2.84 = 2.84 0.8x + x2 = 2.84 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 2.84 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 2.84 + 0.16 Combine like terms: 2.84 + 0.16 = 3 0.16 + 0.8x + x2 = 3 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 0.4) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 0.4 = 1.732050808 Simplifying x + 0.4 = 1.732050808 Reorder the terms: 0.4 + x = 1.732050808 Solving 0.4 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.732050808 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.732050808 + -0.4 x = 1.732050808 + -0.4 Combine like terms: 1.732050808 + -0.4 = 1.332050808 x = 1.332050808 Simplifying x = 1.332050808Subproblem 2
x + 0.4 = -1.732050808 Simplifying x + 0.4 = -1.732050808 Reorder the terms: 0.4 + x = -1.732050808 Solving 0.4 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.732050808 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.732050808 + -0.4 x = -1.732050808 + -0.4 Combine like terms: -1.732050808 + -0.4 = -2.132050808 x = -2.132050808 Simplifying x = -2.132050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.332050808, -2.132050808}
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