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Simplifying 25x2 + -20x + -13 = 0 Reorder the terms: -13 + -20x + 25x2 = 0 Solving -13 + -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'. -0.52 + -0.8x + x2 = 0 Move the constant term to the right: Add '0.52' to each side of the equation. -0.52 + -0.8x + 0.52 + x2 = 0 + 0.52 Reorder the terms: -0.52 + 0.52 + -0.8x + x2 = 0 + 0.52 Combine like terms: -0.52 + 0.52 = 0.00 0.00 + -0.8x + x2 = 0 + 0.52 -0.8x + x2 = 0 + 0.52 Combine like terms: 0 + 0.52 = 0.52 -0.8x + x2 = 0.52 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 = 0.52 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 0.52 + 0.16 Combine like terms: 0.52 + 0.16 = 0.68 0.16 + -0.8x + x2 = 0.68 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.68 Calculate the square root of the right side: 0.824621125 Break this problem into two subproblems by setting (x + -0.4) equal to 0.824621125 and -0.824621125.Subproblem 1
x + -0.4 = 0.824621125 Simplifying x + -0.4 = 0.824621125 Reorder the terms: -0.4 + x = 0.824621125 Solving -0.4 + x = 0.824621125 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 = 0.824621125 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.824621125 + 0.4 x = 0.824621125 + 0.4 Combine like terms: 0.824621125 + 0.4 = 1.224621125 x = 1.224621125 Simplifying x = 1.224621125Subproblem 2
x + -0.4 = -0.824621125 Simplifying x + -0.4 = -0.824621125 Reorder the terms: -0.4 + x = -0.824621125 Solving -0.4 + x = -0.824621125 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 = -0.824621125 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.824621125 + 0.4 x = -0.824621125 + 0.4 Combine like terms: -0.824621125 + 0.4 = -0.424621125 x = -0.424621125 Simplifying x = -0.424621125Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.224621125, -0.424621125}
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