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Simplifying x^{2}+ 4x = 2x^{2}+ 7x + -6 Reorder the terms: 4x + x^{2}= 2x^{2}+ 7x + -6 Reorder the terms: 4x + x^{2}= -6 + 7x + 2x^{2}Solving 4x + x^{2}= -6 + 7x + 2x^{2}Solving for variable 'x'. Reorder the terms: 6 + 4x + -7x + x^{2}+ -2x^{2}= -6 + 7x + 2x^{2}+ 6 + -7x + -2x^{2}Combine like terms: 4x + -7x = -3x 6 + -3x + x^{2}+ -2x^{2}= -6 + 7x + 2x^{2}+ 6 + -7x + -2x^{2}Combine like terms: x^{2}+ -2x^{2}= -1x^{2}6 + -3x + -1x^{2}= -6 + 7x + 2x^{2}+ 6 + -7x + -2x^{2}Reorder the terms: 6 + -3x + -1x^{2}= -6 + 6 + 7x + -7x + 2x^{2}+ -2x^{2}Combine like terms: -6 + 6 = 0 6 + -3x + -1x^{2}= 0 + 7x + -7x + 2x^{2}+ -2x^{2}6 + -3x + -1x^{2}= 7x + -7x + 2x^{2}+ -2x^{2}Combine like terms: 7x + -7x = 0 6 + -3x + -1x^{2}= 0 + 2x^{2}+ -2x^{2}6 + -3x + -1x^{2}= 2x^{2}+ -2x^{2}Combine like terms: 2x^{2}+ -2x^{2}= 0 6 + -3x + -1x^{2}= 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + 3x + x^{2}= 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 3x + 6 + x^{2}= 0 + 6 Reorder the terms: -6 + 6 + 3x + x^{2}= 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3x + x^{2}= 0 + 6 3x + x^{2}= 0 + 6 Combine like terms: 0 + 6 = 6 3x + x^{2}= 6 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x^{2}= 6 + 2.25 Reorder the terms: 2.25 + 3x + x^{2}= 6 + 2.25 Combine like terms: 6 + 2.25 = 8.25 2.25 + 3x + x^{2}= 8.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + 1.5) equal to 2.872281323 and -2.872281323.## Subproblem 1

x + 1.5 = 2.872281323 Simplifying x + 1.5 = 2.872281323 Reorder the terms: 1.5 + x = 2.872281323 Solving 1.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.872281323 + -1.5 x = 2.872281323 + -1.5 Combine like terms: 2.872281323 + -1.5 = 1.372281323 x = 1.372281323 Simplifying x = 1.372281323## Subproblem 2

x + 1.5 = -2.872281323 Simplifying x + 1.5 = -2.872281323 Reorder the terms: 1.5 + x = -2.872281323 Solving 1.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.872281323 + -1.5 x = -2.872281323 + -1.5 Combine like terms: -2.872281323 + -1.5 = -4.372281323 x = -4.372281323 Simplifying x = -4.372281323## Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.372281323, -4.372281323}

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