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Simplifying 2(x + 5)(x + 2) = 190 Reorder the terms: 2(5 + x)(x + 2) = 190 Reorder the terms: 2(5 + x)(2 + x) = 190 Multiply (5 + x) * (2 + x) 2(5(2 + x) + x(2 + x)) = 190 2((2 * 5 + x * 5) + x(2 + x)) = 190 2((10 + 5x) + x(2 + x)) = 190 2(10 + 5x + (2 * x + x * x)) = 190 2(10 + 5x + (2x + x2)) = 190 Combine like terms: 5x + 2x = 7x 2(10 + 7x + x2) = 190 (10 * 2 + 7x * 2 + x2 * 2) = 190 (20 + 14x + 2x2) = 190 Solving 20 + 14x + 2x2 = 190 Solving for variable 'x'. Reorder the terms: 20 + -190 + 14x + 2x2 = 190 + -190 Combine like terms: 20 + -190 = -170 -170 + 14x + 2x2 = 190 + -190 Combine like terms: 190 + -190 = 0 -170 + 14x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-85 + 7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-85 + 7x + x2)' equal to zero and attempt to solve: Simplifying -85 + 7x + x2 = 0 Solving -85 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + 7x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + 7x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + 7x + x2 = 0 + 85 7x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 7x + x2 = 85 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 85 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 85 + 12.25 Combine like terms: 85 + 12.25 = 97.25 12.25 + 7x + x2 = 97.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 97.25 Calculate the square root of the right side: 9.861541462 Break this problem into two subproblems by setting (x + 3.5) equal to 9.861541462 and -9.861541462.Subproblem 1
x + 3.5 = 9.861541462 Simplifying x + 3.5 = 9.861541462 Reorder the terms: 3.5 + x = 9.861541462 Solving 3.5 + x = 9.861541462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 9.861541462 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.861541462 + -3.5 x = 9.861541462 + -3.5 Combine like terms: 9.861541462 + -3.5 = 6.361541462 x = 6.361541462 Simplifying x = 6.361541462Subproblem 2
x + 3.5 = -9.861541462 Simplifying x + 3.5 = -9.861541462 Reorder the terms: 3.5 + x = -9.861541462 Solving 3.5 + x = -9.861541462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -9.861541462 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.861541462 + -3.5 x = -9.861541462 + -3.5 Combine like terms: -9.861541462 + -3.5 = -13.361541462 x = -13.361541462 Simplifying x = -13.361541462Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.361541462, -13.361541462}Solution
x = {6.361541462, -13.361541462}
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