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Simplifying 3x2 + 18x = 8 Reorder the terms: 18x + 3x2 = 8 Solving 18x + 3x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 18x + 3x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + 6x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 6x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 6x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 6x + x2 = 0 + 2.666666667 6x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 6x + x2 = 2.666666667 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 = 2.666666667 + 9 Reorder the terms: 9 + 6x + x2 = 2.666666667 + 9 Combine like terms: 2.666666667 + 9 = 11.666666667 9 + 6x + x2 = 11.666666667 Factor a perfect square on the left side: (x + 3)(x + 3) = 11.666666667 Calculate the square root of the right side: 3.415650255 Break this problem into two subproblems by setting (x + 3) equal to 3.415650255 and -3.415650255.Subproblem 1
x + 3 = 3.415650255 Simplifying x + 3 = 3.415650255 Reorder the terms: 3 + x = 3.415650255 Solving 3 + x = 3.415650255 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 = 3.415650255 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.415650255 + -3 x = 3.415650255 + -3 Combine like terms: 3.415650255 + -3 = 0.415650255 x = 0.415650255 Simplifying x = 0.415650255Subproblem 2
x + 3 = -3.415650255 Simplifying x + 3 = -3.415650255 Reorder the terms: 3 + x = -3.415650255 Solving 3 + x = -3.415650255 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 = -3.415650255 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.415650255 + -3 x = -3.415650255 + -3 Combine like terms: -3.415650255 + -3 = -6.415650255 x = -6.415650255 Simplifying x = -6.415650255Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.415650255, -6.415650255}
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