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Simplifying 25x2 + -124x + 144 = 0 Reorder the terms: 144 + -124x + 25x2 = 0 Solving 144 + -124x + 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'. 5.76 + -4.96x + x2 = 0 Move the constant term to the right: Add '-5.76' to each side of the equation. 5.76 + -4.96x + -5.76 + x2 = 0 + -5.76 Reorder the terms: 5.76 + -5.76 + -4.96x + x2 = 0 + -5.76 Combine like terms: 5.76 + -5.76 = 0.00 0.00 + -4.96x + x2 = 0 + -5.76 -4.96x + x2 = 0 + -5.76 Combine like terms: 0 + -5.76 = -5.76 -4.96x + x2 = -5.76 The x term is -4.96x. Take half its coefficient (-2.48). Square it (6.1504) and add it to both sides. Add '6.1504' to each side of the equation. -4.96x + 6.1504 + x2 = -5.76 + 6.1504 Reorder the terms: 6.1504 + -4.96x + x2 = -5.76 + 6.1504 Combine like terms: -5.76 + 6.1504 = 0.3904 6.1504 + -4.96x + x2 = 0.3904 Factor a perfect square on the left side: (x + -2.48)(x + -2.48) = 0.3904 Calculate the square root of the right side: 0.624819974 Break this problem into two subproblems by setting (x + -2.48) equal to 0.624819974 and -0.624819974.Subproblem 1
x + -2.48 = 0.624819974 Simplifying x + -2.48 = 0.624819974 Reorder the terms: -2.48 + x = 0.624819974 Solving -2.48 + x = 0.624819974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.48' to each side of the equation. -2.48 + 2.48 + x = 0.624819974 + 2.48 Combine like terms: -2.48 + 2.48 = 0.00 0.00 + x = 0.624819974 + 2.48 x = 0.624819974 + 2.48 Combine like terms: 0.624819974 + 2.48 = 3.104819974 x = 3.104819974 Simplifying x = 3.104819974Subproblem 2
x + -2.48 = -0.624819974 Simplifying x + -2.48 = -0.624819974 Reorder the terms: -2.48 + x = -0.624819974 Solving -2.48 + x = -0.624819974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.48' to each side of the equation. -2.48 + 2.48 + x = -0.624819974 + 2.48 Combine like terms: -2.48 + 2.48 = 0.00 0.00 + x = -0.624819974 + 2.48 x = -0.624819974 + 2.48 Combine like terms: -0.624819974 + 2.48 = 1.855180026 x = 1.855180026 Simplifying x = 1.855180026Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.104819974, 1.855180026}
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