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Simplifying 2x(x + -3) = 3(x + 4) Reorder the terms: 2x(-3 + x) = 3(x + 4) (-3 * 2x + x * 2x) = 3(x + 4) (-6x + 2x2) = 3(x + 4) Reorder the terms: -6x + 2x2 = 3(4 + x) -6x + 2x2 = (4 * 3 + x * 3) -6x + 2x2 = (12 + 3x) Solving -6x + 2x2 = 12 + 3x Solving for variable 'x'. Reorder the terms: -12 + -6x + -3x + 2x2 = 12 + 3x + -12 + -3x Combine like terms: -6x + -3x = -9x -12 + -9x + 2x2 = 12 + 3x + -12 + -3x Reorder the terms: -12 + -9x + 2x2 = 12 + -12 + 3x + -3x Combine like terms: 12 + -12 = 0 -12 + -9x + 2x2 = 0 + 3x + -3x -12 + -9x + 2x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -12 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -4.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -4.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -4.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -4.5x + x2 = 0 + 6 -4.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -4.5x + x2 = 6 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 6 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 6 + 5.0625 Combine like terms: 6 + 5.0625 = 11.0625 5.0625 + -4.5x + x2 = 11.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (x + -2.25) equal to 3.326033674 and -3.326033674.Subproblem 1
x + -2.25 = 3.326033674 Simplifying x + -2.25 = 3.326033674 Reorder the terms: -2.25 + x = 3.326033674 Solving -2.25 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 3.326033674 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 3.326033674 + 2.25 x = 3.326033674 + 2.25 Combine like terms: 3.326033674 + 2.25 = 5.576033674 x = 5.576033674 Simplifying x = 5.576033674Subproblem 2
x + -2.25 = -3.326033674 Simplifying x + -2.25 = -3.326033674 Reorder the terms: -2.25 + x = -3.326033674 Solving -2.25 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -3.326033674 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -3.326033674 + 2.25 x = -3.326033674 + 2.25 Combine like terms: -3.326033674 + 2.25 = -1.076033674 x = -1.076033674 Simplifying x = -1.076033674Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.576033674, -1.076033674}
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