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Simplifying 18x + 36 = 8x2 + 50x + 32 Reorder the terms: 36 + 18x = 8x2 + 50x + 32 Reorder the terms: 36 + 18x = 32 + 50x + 8x2 Solving 36 + 18x = 32 + 50x + 8x2 Solving for variable 'x'. Reorder the terms: 36 + -32 + 18x + -50x + -8x2 = 32 + 50x + 8x2 + -32 + -50x + -8x2 Combine like terms: 36 + -32 = 4 4 + 18x + -50x + -8x2 = 32 + 50x + 8x2 + -32 + -50x + -8x2 Combine like terms: 18x + -50x = -32x 4 + -32x + -8x2 = 32 + 50x + 8x2 + -32 + -50x + -8x2 Reorder the terms: 4 + -32x + -8x2 = 32 + -32 + 50x + -50x + 8x2 + -8x2 Combine like terms: 32 + -32 = 0 4 + -32x + -8x2 = 0 + 50x + -50x + 8x2 + -8x2 4 + -32x + -8x2 = 50x + -50x + 8x2 + -8x2 Combine like terms: 50x + -50x = 0 4 + -32x + -8x2 = 0 + 8x2 + -8x2 4 + -32x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 4 + -32x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1 + -8x + -2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -8x + -2x2)' equal to zero and attempt to solve: Simplifying 1 + -8x + -2x2 = 0 Solving 1 + -8x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + 4x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 4x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 4x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 4x + x2 = 0 + 0.5 4x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 4x + x2 = 0.5 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 = 0.5 + 4 Reorder the terms: 4 + 4x + x2 = 0.5 + 4 Combine like terms: 0.5 + 4 = 4.5 4 + 4x + x2 = 4.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x + 2) equal to 2.121320344 and -2.121320344.Subproblem 1
x + 2 = 2.121320344 Simplifying x + 2 = 2.121320344 Reorder the terms: 2 + x = 2.121320344 Solving 2 + x = 2.121320344 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 = 2.121320344 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.121320344 + -2 x = 2.121320344 + -2 Combine like terms: 2.121320344 + -2 = 0.121320344 x = 0.121320344 Simplifying x = 0.121320344Subproblem 2
x + 2 = -2.121320344 Simplifying x + 2 = -2.121320344 Reorder the terms: 2 + x = -2.121320344 Solving 2 + x = -2.121320344 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 = -2.121320344 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.121320344 + -2 x = -2.121320344 + -2 Combine like terms: -2.121320344 + -2 = -4.121320344 x = -4.121320344 Simplifying x = -4.121320344Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.121320344, -4.121320344}Solution
x = {0.121320344, -4.121320344}
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