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Simplifying (2x + 2)(x + 2) = 100 Reorder the terms: (2 + 2x)(x + 2) = 100 Reorder the terms: (2 + 2x)(2 + x) = 100 Multiply (2 + 2x) * (2 + x) (2(2 + x) + 2x * (2 + x)) = 100 ((2 * 2 + x * 2) + 2x * (2 + x)) = 100 ((4 + 2x) + 2x * (2 + x)) = 100 (4 + 2x + (2 * 2x + x * 2x)) = 100 (4 + 2x + (4x + 2x2)) = 100 Combine like terms: 2x + 4x = 6x (4 + 6x + 2x2) = 100 Solving 4 + 6x + 2x2 = 100 Solving for variable 'x'. Reorder the terms: 4 + -100 + 6x + 2x2 = 100 + -100 Combine like terms: 4 + -100 = -96 -96 + 6x + 2x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -96 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-48 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-48 + 3x + x2)' equal to zero and attempt to solve: Simplifying -48 + 3x + x2 = 0 Solving -48 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 3x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 3x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 3x + x2 = 0 + 48 3x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 3x + x2 = 48 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 = 48 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 48 + 2.25 Combine like terms: 48 + 2.25 = 50.25 2.25 + 3x + x2 = 50.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + 1.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + 1.5 = 7.088723439 Simplifying x + 1.5 = 7.088723439 Reorder the terms: 1.5 + x = 7.088723439 Solving 1.5 + x = 7.088723439 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 = 7.088723439 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.088723439 + -1.5 x = 7.088723439 + -1.5 Combine like terms: 7.088723439 + -1.5 = 5.588723439 x = 5.588723439 Simplifying x = 5.588723439Subproblem 2
x + 1.5 = -7.088723439 Simplifying x + 1.5 = -7.088723439 Reorder the terms: 1.5 + x = -7.088723439 Solving 1.5 + x = -7.088723439 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 = -7.088723439 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.088723439 + -1.5 x = -7.088723439 + -1.5 Combine like terms: -7.088723439 + -1.5 = -8.588723439 x = -8.588723439 Simplifying x = -8.588723439Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.588723439, -8.588723439}Solution
x = {5.588723439, -8.588723439}
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