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Simplifying 3(5 + -4x + -3 + 3x) = 2x(4x + -3 + -3x + -3) Reorder the terms: 3(5 + -3 + -4x + 3x) = 2x(4x + -3 + -3x + -3) Combine like terms: 5 + -3 = 2 3(2 + -4x + 3x) = 2x(4x + -3 + -3x + -3) Combine like terms: -4x + 3x = -1x 3(2 + -1x) = 2x(4x + -3 + -3x + -3) (2 * 3 + -1x * 3) = 2x(4x + -3 + -3x + -3) (6 + -3x) = 2x(4x + -3 + -3x + -3) Reorder the terms: 6 + -3x = 2x(-3 + -3 + 4x + -3x) Combine like terms: -3 + -3 = -6 6 + -3x = 2x(-6 + 4x + -3x) Combine like terms: 4x + -3x = 1x 6 + -3x = 2x(-6 + 1x) 6 + -3x = (-6 * 2x + 1x * 2x) 6 + -3x = (-12x + 2x2) Solving 6 + -3x = -12x + 2x2 Solving for variable 'x'. Combine like terms: -3x + 12x = 9x 6 + 9x + -2x2 = -12x + 2x2 + 12x + -2x2 Reorder the terms: 6 + 9x + -2x2 = -12x + 12x + 2x2 + -2x2 Combine like terms: -12x + 12x = 0 6 + 9x + -2x2 = 0 + 2x2 + -2x2 6 + 9x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 6 + 9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3 + -4.5x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -4.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -4.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4.5x + x2 = 0 + 3 -4.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4.5x + x2 = 3 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 = 3 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 3 + 5.0625 Combine like terms: 3 + 5.0625 = 8.0625 5.0625 + -4.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + -2.25) equal to 2.839454173 and -2.839454173.Subproblem 1
x + -2.25 = 2.839454173 Simplifying x + -2.25 = 2.839454173 Reorder the terms: -2.25 + x = 2.839454173 Solving -2.25 + x = 2.839454173 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 = 2.839454173 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.839454173 + 2.25 x = 2.839454173 + 2.25 Combine like terms: 2.839454173 + 2.25 = 5.089454173 x = 5.089454173 Simplifying x = 5.089454173Subproblem 2
x + -2.25 = -2.839454173 Simplifying x + -2.25 = -2.839454173 Reorder the terms: -2.25 + x = -2.839454173 Solving -2.25 + x = -2.839454173 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 = -2.839454173 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.839454173 + 2.25 x = -2.839454173 + 2.25 Combine like terms: -2.839454173 + 2.25 = -0.589454173 x = -0.589454173 Simplifying x = -0.589454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.089454173, -0.589454173}
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