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Simplifying 6x2 + -45x + 25 = 0 Reorder the terms: 25 + -45x + 6x2 = 0 Solving 25 + -45x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 4.166666667 + -7.5x + x2 = 0 Move the constant term to the right: Add '-4.166666667' to each side of the equation. 4.166666667 + -7.5x + -4.166666667 + x2 = 0 + -4.166666667 Reorder the terms: 4.166666667 + -4.166666667 + -7.5x + x2 = 0 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + -7.5x + x2 = 0 + -4.166666667 -7.5x + x2 = 0 + -4.166666667 Combine like terms: 0 + -4.166666667 = -4.166666667 -7.5x + x2 = -4.166666667 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -4.166666667 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -4.166666667 + 14.0625 Combine like terms: -4.166666667 + 14.0625 = 9.895833333 14.0625 + -7.5x + x2 = 9.895833333 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 9.895833333 Calculate the square root of the right side: 3.145764348 Break this problem into two subproblems by setting (x + -3.75) equal to 3.145764348 and -3.145764348.Subproblem 1
x + -3.75 = 3.145764348 Simplifying x + -3.75 = 3.145764348 Reorder the terms: -3.75 + x = 3.145764348 Solving -3.75 + x = 3.145764348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 3.145764348 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 3.145764348 + 3.75 x = 3.145764348 + 3.75 Combine like terms: 3.145764348 + 3.75 = 6.895764348 x = 6.895764348 Simplifying x = 6.895764348Subproblem 2
x + -3.75 = -3.145764348 Simplifying x + -3.75 = -3.145764348 Reorder the terms: -3.75 + x = -3.145764348 Solving -3.75 + x = -3.145764348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -3.145764348 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -3.145764348 + 3.75 x = -3.145764348 + 3.75 Combine like terms: -3.145764348 + 3.75 = 0.604235652 x = 0.604235652 Simplifying x = 0.604235652Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.895764348, 0.604235652}
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