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Simplifying 3x2 + -18x + 25 = 0 Reorder the terms: 25 + -18x + 3x2 = 0 Solving 25 + -18x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8.333333333 + -6x + x2 = 0 Move the constant term to the right: Add '-8.333333333' to each side of the equation. 8.333333333 + -6x + -8.333333333 + x2 = 0 + -8.333333333 Reorder the terms: 8.333333333 + -8.333333333 + -6x + x2 = 0 + -8.333333333 Combine like terms: 8.333333333 + -8.333333333 = 0.000000000 0.000000000 + -6x + x2 = 0 + -8.333333333 -6x + x2 = 0 + -8.333333333 Combine like terms: 0 + -8.333333333 = -8.333333333 -6x + x2 = -8.333333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -8.333333333 + 9 Reorder the terms: 9 + -6x + x2 = -8.333333333 + 9 Combine like terms: -8.333333333 + 9 = 0.666666667 9 + -6x + x2 = 0.666666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 0.666666667 Calculate the square root of the right side: 0.816496581 Break this problem into two subproblems by setting (x + -3) equal to 0.816496581 and -0.816496581.Subproblem 1
x + -3 = 0.816496581 Simplifying x + -3 = 0.816496581 Reorder the terms: -3 + x = 0.816496581 Solving -3 + x = 0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0.816496581 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0.816496581 + 3 x = 0.816496581 + 3 Combine like terms: 0.816496581 + 3 = 3.816496581 x = 3.816496581 Simplifying x = 3.816496581Subproblem 2
x + -3 = -0.816496581 Simplifying x + -3 = -0.816496581 Reorder the terms: -3 + x = -0.816496581 Solving -3 + x = -0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -0.816496581 + 3 Combine like terms: -3 + 3 = 0 0 + x = -0.816496581 + 3 x = -0.816496581 + 3 Combine like terms: -0.816496581 + 3 = 2.183503419 x = 2.183503419 Simplifying x = 2.183503419Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.816496581, 2.183503419}
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