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Simplifying 2x2 + 3x + 4x + 6 = 18x + 9 Reorder the terms: 6 + 3x + 4x + 2x2 = 18x + 9 Combine like terms: 3x + 4x = 7x 6 + 7x + 2x2 = 18x + 9 Reorder the terms: 6 + 7x + 2x2 = 9 + 18x Solving 6 + 7x + 2x2 = 9 + 18x Solving for variable 'x'. Reorder the terms: 6 + -9 + 7x + -18x + 2x2 = 9 + 18x + -9 + -18x Combine like terms: 6 + -9 = -3 -3 + 7x + -18x + 2x2 = 9 + 18x + -9 + -18x Combine like terms: 7x + -18x = -11x -3 + -11x + 2x2 = 9 + 18x + -9 + -18x Reorder the terms: -3 + -11x + 2x2 = 9 + -9 + 18x + -18x Combine like terms: 9 + -9 = 0 -3 + -11x + 2x2 = 0 + 18x + -18x -3 + -11x + 2x2 = 18x + -18x Combine like terms: 18x + -18x = 0 -3 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -5.5x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -5.5x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -5.5x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -5.5x + x2 = 0 + 1.5 -5.5x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -5.5x + x2 = 1.5 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = 1.5 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 1.5 + 7.5625 Combine like terms: 1.5 + 7.5625 = 9.0625 7.5625 + -5.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -2.75) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -2.75 = 3.010398645 Simplifying x + -2.75 = 3.010398645 Reorder the terms: -2.75 + x = 3.010398645 Solving -2.75 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 3.010398645 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.010398645 + 2.75 x = 3.010398645 + 2.75 Combine like terms: 3.010398645 + 2.75 = 5.760398645 x = 5.760398645 Simplifying x = 5.760398645Subproblem 2
x + -2.75 = -3.010398645 Simplifying x + -2.75 = -3.010398645 Reorder the terms: -2.75 + x = -3.010398645 Solving -2.75 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -3.010398645 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.010398645 + 2.75 x = -3.010398645 + 2.75 Combine like terms: -3.010398645 + 2.75 = -0.260398645 x = -0.260398645 Simplifying x = -0.260398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.760398645, -0.260398645}
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