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Simplifying 2x + 4x2 = 69 Solving 2x + 4x2 = 69 Solving for variable 'x'. Reorder the terms: -69 + 2x + 4x2 = 69 + -69 Combine like terms: 69 + -69 = 0 -69 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -17.25 + 0.5x + x2 = 0 Move the constant term to the right: Add '17.25' to each side of the equation. -17.25 + 0.5x + 17.25 + x2 = 0 + 17.25 Reorder the terms: -17.25 + 17.25 + 0.5x + x2 = 0 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + 0.5x + x2 = 0 + 17.25 0.5x + x2 = 0 + 17.25 Combine like terms: 0 + 17.25 = 17.25 0.5x + x2 = 17.25 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 17.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 17.25 + 0.0625 Combine like terms: 17.25 + 0.0625 = 17.3125 0.0625 + 0.5x + x2 = 17.3125 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 17.3125 Calculate the square root of the right side: 4.160829244 Break this problem into two subproblems by setting (x + 0.25) equal to 4.160829244 and -4.160829244.Subproblem 1
x + 0.25 = 4.160829244 Simplifying x + 0.25 = 4.160829244 Reorder the terms: 0.25 + x = 4.160829244 Solving 0.25 + x = 4.160829244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 4.160829244 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 4.160829244 + -0.25 x = 4.160829244 + -0.25 Combine like terms: 4.160829244 + -0.25 = 3.910829244 x = 3.910829244 Simplifying x = 3.910829244Subproblem 2
x + 0.25 = -4.160829244 Simplifying x + 0.25 = -4.160829244 Reorder the terms: 0.25 + x = -4.160829244 Solving 0.25 + x = -4.160829244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -4.160829244 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -4.160829244 + -0.25 x = -4.160829244 + -0.25 Combine like terms: -4.160829244 + -0.25 = -4.410829244 x = -4.410829244 Simplifying x = -4.410829244Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.910829244, -4.410829244}
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