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Simplifying 2x(x + -3) = 6 Reorder the terms: 2x(-3 + x) = 6 (-3 * 2x + x * 2x) = 6 (-6x + 2x^{2}) = 6 Solving -6x + 2x^{2}= 6 Solving for variable 'x'. Reorder the terms: -6 + -6x + 2x^{2}= 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -6x + 2x^{2}= 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -3x + x^{2}) = 0 Ignore the factor 2.## Subproblem 1

Set the factor '(-3 + -3x + x^{2})' equal to zero and attempt to solve: Simplifying -3 + -3x + x^{2}= 0 Solving -3 + -3x + x^{2}= 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -3x + 3 + x^{2}= 0 + 3 Reorder the terms: -3 + 3 + -3x + x^{2}= 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3x + x^{2}= 0 + 3 -3x + x^{2}= 0 + 3 Combine like terms: 0 + 3 = 3 -3x + x^{2}= 3 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}= 3 + 2.25 Reorder the terms: 2.25 + -3x + x^{2}= 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + -3x + x^{2}= 5.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -1.5) equal to 2.291287847 and -2.291287847.## Subproblem 1

x + -1.5 = 2.291287847 Simplifying x + -1.5 = 2.291287847 Reorder the terms: -1.5 + x = 2.291287847 Solving -1.5 + x = 2.291287847 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 = 2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.291287847 + 1.5 x = 2.291287847 + 1.5 Combine like terms: 2.291287847 + 1.5 = 3.791287847 x = 3.791287847 Simplifying x = 3.791287847## Subproblem 2

x + -1.5 = -2.291287847 Simplifying x + -1.5 = -2.291287847 Reorder the terms: -1.5 + x = -2.291287847 Solving -1.5 + x = -2.291287847 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 = -2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.291287847 + 1.5 x = -2.291287847 + 1.5 Combine like terms: -2.291287847 + 1.5 = -0.791287847 x = -0.791287847 Simplifying x = -0.791287847## Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.791287847, -0.791287847}## Solution

x = {3.791287847, -0.791287847}

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