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Simplifying 25x2 + -20x + -59 = 0 Reorder the terms: -59 + -20x + 25x2 = 0 Solving -59 + -20x + 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'. -2.36 + -0.8x + x2 = 0 Move the constant term to the right: Add '2.36' to each side of the equation. -2.36 + -0.8x + 2.36 + x2 = 0 + 2.36 Reorder the terms: -2.36 + 2.36 + -0.8x + x2 = 0 + 2.36 Combine like terms: -2.36 + 2.36 = 0.00 0.00 + -0.8x + x2 = 0 + 2.36 -0.8x + x2 = 0 + 2.36 Combine like terms: 0 + 2.36 = 2.36 -0.8x + x2 = 2.36 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 = 2.36 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 2.36 + 0.16 Combine like terms: 2.36 + 0.16 = 2.52 0.16 + -0.8x + x2 = 2.52 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 2.52 Calculate the square root of the right side: 1.587450787 Break this problem into two subproblems by setting (x + -0.4) equal to 1.587450787 and -1.587450787.Subproblem 1
x + -0.4 = 1.587450787 Simplifying x + -0.4 = 1.587450787 Reorder the terms: -0.4 + x = 1.587450787 Solving -0.4 + x = 1.587450787 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 = 1.587450787 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.587450787 + 0.4 x = 1.587450787 + 0.4 Combine like terms: 1.587450787 + 0.4 = 1.987450787 x = 1.987450787 Simplifying x = 1.987450787Subproblem 2
x + -0.4 = -1.587450787 Simplifying x + -0.4 = -1.587450787 Reorder the terms: -0.4 + x = -1.587450787 Solving -0.4 + x = -1.587450787 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 = -1.587450787 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.587450787 + 0.4 x = -1.587450787 + 0.4 Combine like terms: -1.587450787 + 0.4 = -1.187450787 x = -1.187450787 Simplifying x = -1.187450787Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.987450787, -1.187450787}
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