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Simplifying (x + -3)(x + -2) = 7x + 30 Reorder the terms: (-3 + x)(x + -2) = 7x + 30 Reorder the terms: (-3 + x)(-2 + x) = 7x + 30 Multiply (-3 + x) * (-2 + x) (-3(-2 + x) + x(-2 + x)) = 7x + 30 ((-2 * -3 + x * -3) + x(-2 + x)) = 7x + 30 ((6 + -3x) + x(-2 + x)) = 7x + 30 (6 + -3x + (-2 * x + x * x)) = 7x + 30 (6 + -3x + (-2x + x2)) = 7x + 30 Combine like terms: -3x + -2x = -5x (6 + -5x + x2) = 7x + 30 Reorder the terms: 6 + -5x + x2 = 30 + 7x Solving 6 + -5x + x2 = 30 + 7x Solving for variable 'x'. Reorder the terms: 6 + -30 + -5x + -7x + x2 = 30 + 7x + -30 + -7x Combine like terms: 6 + -30 = -24 -24 + -5x + -7x + x2 = 30 + 7x + -30 + -7x Combine like terms: -5x + -7x = -12x -24 + -12x + x2 = 30 + 7x + -30 + -7x Reorder the terms: -24 + -12x + x2 = 30 + -30 + 7x + -7x Combine like terms: 30 + -30 = 0 -24 + -12x + x2 = 0 + 7x + -7x -24 + -12x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -24 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -12x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -12x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -12x + x2 = 0 + 24 -12x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -12x + x2 = 24 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 24 + 36 Reorder the terms: 36 + -12x + x2 = 24 + 36 Combine like terms: 24 + 36 = 60 36 + -12x + x2 = 60 Factor a perfect square on the left side: (x + -6)(x + -6) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -6) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -6 = 7.745966692 Simplifying x + -6 = 7.745966692 Reorder the terms: -6 + x = 7.745966692 Solving -6 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.745966692 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.745966692 + 6 x = 7.745966692 + 6 Combine like terms: 7.745966692 + 6 = 13.745966692 x = 13.745966692 Simplifying x = 13.745966692Subproblem 2
x + -6 = -7.745966692 Simplifying x + -6 = -7.745966692 Reorder the terms: -6 + x = -7.745966692 Solving -6 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.745966692 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.745966692 + 6 x = -7.745966692 + 6 Combine like terms: -7.745966692 + 6 = -1.745966692 x = -1.745966692 Simplifying x = -1.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.745966692, -1.745966692}
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