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Simplifying 3x2 + 18x = 10 Reorder the terms: 18x + 3x2 = 10 Solving 18x + 3x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 18x + 3x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + 6x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 6x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 6x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 6x + x2 = 0 + 3.333333333 6x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 6x + x2 = 3.333333333 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 = 3.333333333 + 9 Reorder the terms: 9 + 6x + x2 = 3.333333333 + 9 Combine like terms: 3.333333333 + 9 = 12.333333333 9 + 6x + x2 = 12.333333333 Factor a perfect square on the left side: (x + 3)(x + 3) = 12.333333333 Calculate the square root of the right side: 3.511884584 Break this problem into two subproblems by setting (x + 3) equal to 3.511884584 and -3.511884584.Subproblem 1
x + 3 = 3.511884584 Simplifying x + 3 = 3.511884584 Reorder the terms: 3 + x = 3.511884584 Solving 3 + x = 3.511884584 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 = 3.511884584 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.511884584 + -3 x = 3.511884584 + -3 Combine like terms: 3.511884584 + -3 = 0.511884584 x = 0.511884584 Simplifying x = 0.511884584Subproblem 2
x + 3 = -3.511884584 Simplifying x + 3 = -3.511884584 Reorder the terms: 3 + x = -3.511884584 Solving 3 + x = -3.511884584 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 = -3.511884584 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.511884584 + -3 x = -3.511884584 + -3 Combine like terms: -3.511884584 + -3 = -6.511884584 x = -6.511884584 Simplifying x = -6.511884584Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.511884584, -6.511884584}
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