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Simplifying (3x + -1)(3x + -1) = 5(x + -2) + (x + 1)(5x + 2) Reorder the terms: (-1 + 3x)(3x + -1) = 5(x + -2) + (x + 1)(5x + 2) Reorder the terms: (-1 + 3x)(-1 + 3x) = 5(x + -2) + (x + 1)(5x + 2) Multiply (-1 + 3x) * (-1 + 3x) (-1(-1 + 3x) + 3x * (-1 + 3x)) = 5(x + -2) + (x + 1)(5x + 2) ((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) = 5(x + -2) + (x + 1)(5x + 2) ((1 + -3x) + 3x * (-1 + 3x)) = 5(x + -2) + (x + 1)(5x + 2) (1 + -3x + (-1 * 3x + 3x * 3x)) = 5(x + -2) + (x + 1)(5x + 2) (1 + -3x + (-3x + 9x2)) = 5(x + -2) + (x + 1)(5x + 2) Combine like terms: -3x + -3x = -6x (1 + -6x + 9x2) = 5(x + -2) + (x + 1)(5x + 2) Reorder the terms: 1 + -6x + 9x2 = 5(-2 + x) + (x + 1)(5x + 2) 1 + -6x + 9x2 = (-2 * 5 + x * 5) + (x + 1)(5x + 2) 1 + -6x + 9x2 = (-10 + 5x) + (x + 1)(5x + 2) Reorder the terms: 1 + -6x + 9x2 = -10 + 5x + (1 + x)(5x + 2) Reorder the terms: 1 + -6x + 9x2 = -10 + 5x + (1 + x)(2 + 5x) Multiply (1 + x) * (2 + 5x) 1 + -6x + 9x2 = -10 + 5x + (1(2 + 5x) + x(2 + 5x)) 1 + -6x + 9x2 = -10 + 5x + ((2 * 1 + 5x * 1) + x(2 + 5x)) 1 + -6x + 9x2 = -10 + 5x + ((2 + 5x) + x(2 + 5x)) 1 + -6x + 9x2 = -10 + 5x + (2 + 5x + (2 * x + 5x * x)) 1 + -6x + 9x2 = -10 + 5x + (2 + 5x + (2x + 5x2)) Combine like terms: 5x + 2x = 7x 1 + -6x + 9x2 = -10 + 5x + (2 + 7x + 5x2) Reorder the terms: 1 + -6x + 9x2 = -10 + 2 + 5x + 7x + 5x2 Combine like terms: -10 + 2 = -8 1 + -6x + 9x2 = -8 + 5x + 7x + 5x2 Combine like terms: 5x + 7x = 12x 1 + -6x + 9x2 = -8 + 12x + 5x2 Solving 1 + -6x + 9x2 = -8 + 12x + 5x2 Solving for variable 'x'. Reorder the terms: 1 + 8 + -6x + -12x + 9x2 + -5x2 = -8 + 12x + 5x2 + 8 + -12x + -5x2 Combine like terms: 1 + 8 = 9 9 + -6x + -12x + 9x2 + -5x2 = -8 + 12x + 5x2 + 8 + -12x + -5x2 Combine like terms: -6x + -12x = -18x 9 + -18x + 9x2 + -5x2 = -8 + 12x + 5x2 + 8 + -12x + -5x2 Combine like terms: 9x2 + -5x2 = 4x2 9 + -18x + 4x2 = -8 + 12x + 5x2 + 8 + -12x + -5x2 Reorder the terms: 9 + -18x + 4x2 = -8 + 8 + 12x + -12x + 5x2 + -5x2 Combine like terms: -8 + 8 = 0 9 + -18x + 4x2 = 0 + 12x + -12x + 5x2 + -5x2 9 + -18x + 4x2 = 12x + -12x + 5x2 + -5x2 Combine like terms: 12x + -12x = 0 9 + -18x + 4x2 = 0 + 5x2 + -5x2 9 + -18x + 4x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 9 + -18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -4.5x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -4.5x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -4.5x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -4.5x + x2 = 0 + -2.25 -4.5x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -4.5x + x2 = -2.25 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 = -2.25 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -2.25 + 5.0625 Combine like terms: -2.25 + 5.0625 = 2.8125 5.0625 + -4.5x + x2 = 2.8125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting (x + -2.25) equal to 1.677050983 and -1.677050983.Subproblem 1
x + -2.25 = 1.677050983 Simplifying x + -2.25 = 1.677050983 Reorder the terms: -2.25 + x = 1.677050983 Solving -2.25 + x = 1.677050983 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 = 1.677050983 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.677050983 + 2.25 x = 1.677050983 + 2.25 Combine like terms: 1.677050983 + 2.25 = 3.927050983 x = 3.927050983 Simplifying x = 3.927050983Subproblem 2
x + -2.25 = -1.677050983 Simplifying x + -2.25 = -1.677050983 Reorder the terms: -2.25 + x = -1.677050983 Solving -2.25 + x = -1.677050983 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 = -1.677050983 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.677050983 + 2.25 x = -1.677050983 + 2.25 Combine like terms: -1.677050983 + 2.25 = 0.572949017 x = 0.572949017 Simplifying x = 0.572949017Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.927050983, 0.572949017}
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