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Simplifying 3x + [-5x(x + 3)] = 8x + (-5x + -9) Reorder the terms: 3x + [-5x(3 + x)] = 8x + (-5x + -9) 3x + [(3 * -5x + x * -5x)] = 8x + (-5x + -9) 3x + [(-15x + -5x2)] = 8x + (-5x + -9) 3x + [-15x + -5x2] = 8x + (-5x + -9) Remove brackets around [-15x + -5x2] 3x + -15x + -5x2 = 8x + (-5x + -9) Combine like terms: 3x + -15x = -12x -12x + -5x2 = 8x + (-5x + -9) Reorder the terms: -12x + -5x2 = 8x + (-9 + -5x) Remove parenthesis around (-9 + -5x) -12x + -5x2 = 8x + -9 + -5x Reorder the terms: -12x + -5x2 = -9 + 8x + -5x Combine like terms: 8x + -5x = 3x -12x + -5x2 = -9 + 3x Solving -12x + -5x2 = -9 + 3x Solving for variable 'x'. Reorder the terms: 9 + -12x + -3x + -5x2 = -9 + 3x + 9 + -3x Combine like terms: -12x + -3x = -15x 9 + -15x + -5x2 = -9 + 3x + 9 + -3x Reorder the terms: 9 + -15x + -5x2 = -9 + 9 + 3x + -3x Combine like terms: -9 + 9 = 0 9 + -15x + -5x2 = 0 + 3x + -3x 9 + -15x + -5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 9 + -15x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.8 + 3x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 3x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 3x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 3x + x2 = 0 + 1.8 3x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 3x + x2 = 1.8 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 + x2 = 1.8 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1.8 + 2.25 Combine like terms: 1.8 + 2.25 = 4.05 2.25 + 3x + x2 = 4.05 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.05 Calculate the square root of the right side: 2.01246118 Break this problem into two subproblems by setting (x + 1.5) equal to 2.01246118 and -2.01246118.Subproblem 1
x + 1.5 = 2.01246118 Simplifying x + 1.5 = 2.01246118 Reorder the terms: 1.5 + x = 2.01246118 Solving 1.5 + x = 2.01246118 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 = 2.01246118 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.01246118 + -1.5 x = 2.01246118 + -1.5 Combine like terms: 2.01246118 + -1.5 = 0.51246118 x = 0.51246118 Simplifying x = 0.51246118Subproblem 2
x + 1.5 = -2.01246118 Simplifying x + 1.5 = -2.01246118 Reorder the terms: 1.5 + x = -2.01246118 Solving 1.5 + x = -2.01246118 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 = -2.01246118 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.01246118 + -1.5 x = -2.01246118 + -1.5 Combine like terms: -2.01246118 + -1.5 = -3.51246118 x = -3.51246118 Simplifying x = -3.51246118Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.51246118, -3.51246118}
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