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Simplifying 3(4 + 2x) = 5x(x + -2) (4 * 3 + 2x * 3) = 5x(x + -2) (12 + 6x) = 5x(x + -2) Reorder the terms: 12 + 6x = 5x(-2 + x) 12 + 6x = (-2 * 5x + x * 5x) 12 + 6x = (-10x + 5x2) Solving 12 + 6x = -10x + 5x2 Solving for variable 'x'. Combine like terms: 6x + 10x = 16x 12 + 16x + -5x2 = -10x + 5x2 + 10x + -5x2 Reorder the terms: 12 + 16x + -5x2 = -10x + 10x + 5x2 + -5x2 Combine like terms: -10x + 10x = 0 12 + 16x + -5x2 = 0 + 5x2 + -5x2 12 + 16x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 12 + 16x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + -3.2x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -3.2x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -3.2x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -3.2x + x2 = 0 + 2.4 -3.2x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -3.2x + x2 = 2.4 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 2.4 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 2.4 + 2.56 Combine like terms: 2.4 + 2.56 = 4.96 2.56 + -3.2x + x2 = 4.96 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 4.96 Calculate the square root of the right side: 2.227105745 Break this problem into two subproblems by setting (x + -1.6) equal to 2.227105745 and -2.227105745.Subproblem 1
x + -1.6 = 2.227105745 Simplifying x + -1.6 = 2.227105745 Reorder the terms: -1.6 + x = 2.227105745 Solving -1.6 + x = 2.227105745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 2.227105745 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 2.227105745 + 1.6 x = 2.227105745 + 1.6 Combine like terms: 2.227105745 + 1.6 = 3.827105745 x = 3.827105745 Simplifying x = 3.827105745Subproblem 2
x + -1.6 = -2.227105745 Simplifying x + -1.6 = -2.227105745 Reorder the terms: -1.6 + x = -2.227105745 Solving -1.6 + x = -2.227105745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -2.227105745 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -2.227105745 + 1.6 x = -2.227105745 + 1.6 Combine like terms: -2.227105745 + 1.6 = -0.627105745 x = -0.627105745 Simplifying x = -0.627105745Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.827105745, -0.627105745}
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