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Simplifying 4x2 + -4x + 1 = 18 Reorder the terms: 1 + -4x + 4x2 = 18 Solving 1 + -4x + 4x2 = 18 Solving for variable 'x'. Reorder the terms: 1 + -18 + -4x + 4x2 = 18 + -18 Combine like terms: 1 + -18 = -17 -17 + -4x + 4x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -17 + -4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + -1x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -1x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -1x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -1x + x2 = 0 + 4.25 -1x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -1x + x2 = 4.25 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 4.25 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 4.25 + 0.25 Combine like terms: 4.25 + 0.25 = 4.5 0.25 + -1x + x2 = 4.5 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x + -0.5) equal to 2.121320344 and -2.121320344.Subproblem 1
x + -0.5 = 2.121320344 Simplifying x + -0.5 = 2.121320344 Reorder the terms: -0.5 + x = 2.121320344 Solving -0.5 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.121320344 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.121320344 + 0.5 x = 2.121320344 + 0.5 Combine like terms: 2.121320344 + 0.5 = 2.621320344 x = 2.621320344 Simplifying x = 2.621320344Subproblem 2
x + -0.5 = -2.121320344 Simplifying x + -0.5 = -2.121320344 Reorder the terms: -0.5 + x = -2.121320344 Solving -0.5 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.121320344 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.121320344 + 0.5 x = -2.121320344 + 0.5 Combine like terms: -2.121320344 + 0.5 = -1.621320344 x = -1.621320344 Simplifying x = -1.621320344Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.621320344, -1.621320344}
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