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Simplifying (5 + x)(2x + -2) = 190 Reorder the terms: (5 + x)(-2 + 2x) = 190 Multiply (5 + x) * (-2 + 2x) (5(-2 + 2x) + x(-2 + 2x)) = 190 ((-2 * 5 + 2x * 5) + x(-2 + 2x)) = 190 ((-10 + 10x) + x(-2 + 2x)) = 190 (-10 + 10x + (-2 * x + 2x * x)) = 190 (-10 + 10x + (-2x + 2x2)) = 190 Combine like terms: 10x + -2x = 8x (-10 + 8x + 2x2) = 190 Solving -10 + 8x + 2x2 = 190 Solving for variable 'x'. Reorder the terms: -10 + -190 + 8x + 2x2 = 190 + -190 Combine like terms: -10 + -190 = -200 -200 + 8x + 2x2 = 190 + -190 Combine like terms: 190 + -190 = 0 -200 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-100 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-100 + 4x + x2)' equal to zero and attempt to solve: Simplifying -100 + 4x + x2 = 0 Solving -100 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 4x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 4x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 4x + x2 = 0 + 100 4x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 4x + x2 = 100 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 100 + 4 Reorder the terms: 4 + 4x + x2 = 100 + 4 Combine like terms: 100 + 4 = 104 4 + 4x + x2 = 104 Factor a perfect square on the left side: (x + 2)(x + 2) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (x + 2) equal to 10.198039027 and -10.198039027.Subproblem 1
x + 2 = 10.198039027 Simplifying x + 2 = 10.198039027 Reorder the terms: 2 + x = 10.198039027 Solving 2 + x = 10.198039027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 10.198039027 + -2 Combine like terms: 2 + -2 = 0 0 + x = 10.198039027 + -2 x = 10.198039027 + -2 Combine like terms: 10.198039027 + -2 = 8.198039027 x = 8.198039027 Simplifying x = 8.198039027Subproblem 2
x + 2 = -10.198039027 Simplifying x + 2 = -10.198039027 Reorder the terms: 2 + x = -10.198039027 Solving 2 + x = -10.198039027 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -10.198039027 + -2 Combine like terms: 2 + -2 = 0 0 + x = -10.198039027 + -2 x = -10.198039027 + -2 Combine like terms: -10.198039027 + -2 = -12.198039027 x = -12.198039027 Simplifying x = -12.198039027Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.198039027, -12.198039027}Solution
x = {8.198039027, -12.198039027}
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