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Simplifying (2 + -1x)(4 + -1x) = 9.5 Multiply (2 + -1x) * (4 + -1x) (2(4 + -1x) + -1x * (4 + -1x)) = 9.5 ((4 * 2 + -1x * 2) + -1x * (4 + -1x)) = 9.5 ((8 + -2x) + -1x * (4 + -1x)) = 9.5 (8 + -2x + (4 * -1x + -1x * -1x)) = 9.5 (8 + -2x + (-4x + 1x2)) = 9.5 Combine like terms: -2x + -4x = -6x (8 + -6x + 1x2) = 9.5 Solving 8 + -6x + 1x2 = 9.5 Solving for variable 'x'. Reorder the terms: 8 + -9.5 + -6x + 1x2 = 9.5 + -9.5 Combine like terms: 8 + -9.5 = -1.5 -1.5 + -6x + 1x2 = 9.5 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 -1.5 + -6x + 1x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -6x + 1.5 + x2 = 0.0 + 1.5 Reorder the terms: -1.5 + 1.5 + -6x + x2 = 0.0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -6x + x2 = 0.0 + 1.5 -6x + x2 = 0.0 + 1.5 Combine like terms: 0.0 + 1.5 = 1.5 -6x + x2 = 1.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 1.5 + 9 Reorder the terms: 9 + -6x + x2 = 1.5 + 9 Combine like terms: 1.5 + 9 = 10.5 9 + -6x + x2 = 10.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 10.5 Calculate the square root of the right side: 3.240370349 Break this problem into two subproblems by setting (x + -3) equal to 3.240370349 and -3.240370349.Subproblem 1
x + -3 = 3.240370349 Simplifying x + -3 = 3.240370349 Reorder the terms: -3 + x = 3.240370349 Solving -3 + x = 3.240370349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.240370349 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.240370349 + 3 x = 3.240370349 + 3 Combine like terms: 3.240370349 + 3 = 6.240370349 x = 6.240370349 Simplifying x = 6.240370349Subproblem 2
x + -3 = -3.240370349 Simplifying x + -3 = -3.240370349 Reorder the terms: -3 + x = -3.240370349 Solving -3 + x = -3.240370349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.240370349 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.240370349 + 3 x = -3.240370349 + 3 Combine like terms: -3.240370349 + 3 = -0.240370349 x = -0.240370349 Simplifying x = -0.240370349Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.240370349, -0.240370349}
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