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Simplifying (3x + -3) * 2 + -1(2x + -7) = (3x + -5)(3x + 5) Reorder the terms: (-3 + 3x) * 2 + -1(2x + -7) = (3x + -5)(3x + 5) Reorder the terms for easier multiplication: 2(-3 + 3x) + -1(2x + -7) = (3x + -5)(3x + 5) (-3 * 2 + 3x * 2) + -1(2x + -7) = (3x + -5)(3x + 5) (-6 + 6x) + -1(2x + -7) = (3x + -5)(3x + 5) Reorder the terms: -6 + 6x + -1(-7 + 2x) = (3x + -5)(3x + 5) -6 + 6x + (-7 * -1 + 2x * -1) = (3x + -5)(3x + 5) -6 + 6x + (7 + -2x) = (3x + -5)(3x + 5) Reorder the terms: -6 + 7 + 6x + -2x = (3x + -5)(3x + 5) Combine like terms: -6 + 7 = 1 1 + 6x + -2x = (3x + -5)(3x + 5) Combine like terms: 6x + -2x = 4x 1 + 4x = (3x + -5)(3x + 5) Reorder the terms: 1 + 4x = (-5 + 3x)(3x + 5) Reorder the terms: 1 + 4x = (-5 + 3x)(5 + 3x) Multiply (-5 + 3x) * (5 + 3x) 1 + 4x = (-5(5 + 3x) + 3x * (5 + 3x)) 1 + 4x = ((5 * -5 + 3x * -5) + 3x * (5 + 3x)) 1 + 4x = ((-25 + -15x) + 3x * (5 + 3x)) 1 + 4x = (-25 + -15x + (5 * 3x + 3x * 3x)) 1 + 4x = (-25 + -15x + (15x + 9x2)) Combine like terms: -15x + 15x = 0 1 + 4x = (-25 + 0 + 9x2) 1 + 4x = (-25 + 9x2) Solving 1 + 4x = -25 + 9x2 Solving for variable 'x'. Reorder the terms: 1 + 25 + 4x + -9x2 = -25 + 9x2 + 25 + -9x2 Combine like terms: 1 + 25 = 26 26 + 4x + -9x2 = -25 + 9x2 + 25 + -9x2 Reorder the terms: 26 + 4x + -9x2 = -25 + 25 + 9x2 + -9x2 Combine like terms: -25 + 25 = 0 26 + 4x + -9x2 = 0 + 9x2 + -9x2 26 + 4x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 26 + 4x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -2.888888889 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '2.888888889' to each side of the equation. -2.888888889 + -0.4444444444x + 2.888888889 + x2 = 0 + 2.888888889 Reorder the terms: -2.888888889 + 2.888888889 + -0.4444444444x + x2 = 0 + 2.888888889 Combine like terms: -2.888888889 + 2.888888889 = 0.000000000 0.000000000 + -0.4444444444x + x2 = 0 + 2.888888889 -0.4444444444x + x2 = 0 + 2.888888889 Combine like terms: 0 + 2.888888889 = 2.888888889 -0.4444444444x + x2 = 2.888888889 The x term is -0.4444444444x. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x + 0.04938271604 + x2 = 2.888888889 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 2.888888889 + 0.04938271604 Combine like terms: 2.888888889 + 0.04938271604 = 2.93827160504 0.04938271604 + -0.4444444444x + x2 = 2.93827160504 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 2.93827160504 Calculate the square root of the right side: 1.714138736 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 1.714138736 and -1.714138736.Subproblem 1
x + -0.2222222222 = 1.714138736 Simplifying x + -0.2222222222 = 1.714138736 Reorder the terms: -0.2222222222 + x = 1.714138736 Solving -0.2222222222 + x = 1.714138736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 1.714138736 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 1.714138736 + 0.2222222222 x = 1.714138736 + 0.2222222222 Combine like terms: 1.714138736 + 0.2222222222 = 1.9363609582 x = 1.9363609582 Simplifying x = 1.9363609582Subproblem 2
x + -0.2222222222 = -1.714138736 Simplifying x + -0.2222222222 = -1.714138736 Reorder the terms: -0.2222222222 + x = -1.714138736 Solving -0.2222222222 + x = -1.714138736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -1.714138736 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -1.714138736 + 0.2222222222 x = -1.714138736 + 0.2222222222 Combine like terms: -1.714138736 + 0.2222222222 = -1.4919165138 x = -1.4919165138 Simplifying x = -1.4919165138Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9363609582, -1.4919165138}
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