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Simplifying 25x2 + -90x + 8 = 0 Reorder the terms: 8 + -90x + 25x2 = 0 Solving 8 + -90x + 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'. 0.32 + -3.6x + x2 = 0 Move the constant term to the right: Add '-0.32' to each side of the equation. 0.32 + -3.6x + -0.32 + x2 = 0 + -0.32 Reorder the terms: 0.32 + -0.32 + -3.6x + x2 = 0 + -0.32 Combine like terms: 0.32 + -0.32 = 0.00 0.00 + -3.6x + x2 = 0 + -0.32 -3.6x + x2 = 0 + -0.32 Combine like terms: 0 + -0.32 = -0.32 -3.6x + x2 = -0.32 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -0.32 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -0.32 + 3.24 Combine like terms: -0.32 + 3.24 = 2.92 3.24 + -3.6x + x2 = 2.92 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 2.92 Calculate the square root of the right side: 1.708800749 Break this problem into two subproblems by setting (x + -1.8) equal to 1.708800749 and -1.708800749.Subproblem 1
x + -1.8 = 1.708800749 Simplifying x + -1.8 = 1.708800749 Reorder the terms: -1.8 + x = 1.708800749 Solving -1.8 + x = 1.708800749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 1.708800749 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 1.708800749 + 1.8 x = 1.708800749 + 1.8 Combine like terms: 1.708800749 + 1.8 = 3.508800749 x = 3.508800749 Simplifying x = 3.508800749Subproblem 2
x + -1.8 = -1.708800749 Simplifying x + -1.8 = -1.708800749 Reorder the terms: -1.8 + x = -1.708800749 Solving -1.8 + x = -1.708800749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -1.708800749 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -1.708800749 + 1.8 x = -1.708800749 + 1.8 Combine like terms: -1.708800749 + 1.8 = 0.091199251 x = 0.091199251 Simplifying x = 0.091199251Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.508800749, 0.091199251}
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