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Simplifying 2x2 + 3x = 6x + 2x + 28 Reorder the terms: 3x + 2x2 = 6x + 2x + 28 Reorder the terms: 3x + 2x2 = 28 + 6x + 2x Combine like terms: 6x + 2x = 8x 3x + 2x2 = 28 + 8x Solving 3x + 2x2 = 28 + 8x Solving for variable 'x'. Reorder the terms: -28 + 3x + -8x + 2x2 = 28 + 8x + -28 + -8x Combine like terms: 3x + -8x = -5x -28 + -5x + 2x2 = 28 + 8x + -28 + -8x Reorder the terms: -28 + -5x + 2x2 = 28 + -28 + 8x + -8x Combine like terms: 28 + -28 = 0 -28 + -5x + 2x2 = 0 + 8x + -8x -28 + -5x + 2x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -28 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14 + -2.5x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -2.5x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -2.5x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -2.5x + x2 = 0 + 14 -2.5x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -2.5x + x2 = 14 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 14 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 14 + 1.5625 Combine like terms: 14 + 1.5625 = 15.5625 1.5625 + -2.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + -1.25) equal to 3.94493346 and -3.94493346.Subproblem 1
x + -1.25 = 3.94493346 Simplifying x + -1.25 = 3.94493346 Reorder the terms: -1.25 + x = 3.94493346 Solving -1.25 + x = 3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 3.94493346 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.94493346 + 1.25 x = 3.94493346 + 1.25 Combine like terms: 3.94493346 + 1.25 = 5.19493346 x = 5.19493346 Simplifying x = 5.19493346Subproblem 2
x + -1.25 = -3.94493346 Simplifying x + -1.25 = -3.94493346 Reorder the terms: -1.25 + x = -3.94493346 Solving -1.25 + x = -3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -3.94493346 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.94493346 + 1.25 x = -3.94493346 + 1.25 Combine like terms: -3.94493346 + 1.25 = -2.69493346 x = -2.69493346 Simplifying x = -2.69493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.19493346, -2.69493346}
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