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Simplifying x = 49x2 + -16 Reorder the terms: x = -16 + 49x2 Solving x = -16 + 49x2 Solving for variable 'x'. Reorder the terms: 16 + x + -49x2 = -16 + 49x2 + 16 + -49x2 Reorder the terms: 16 + x + -49x2 = -16 + 16 + 49x2 + -49x2 Combine like terms: -16 + 16 = 0 16 + x + -49x2 = 0 + 49x2 + -49x2 16 + x + -49x2 = 49x2 + -49x2 Combine like terms: 49x2 + -49x2 = 0 16 + x + -49x2 = 0 Begin completing the square. Divide all terms by -49 the coefficient of the squared term: Divide each side by '-49'. -0.3265306122 + -0.02040816327x + x2 = 0 Move the constant term to the right: Add '0.3265306122' to each side of the equation. -0.3265306122 + -0.02040816327x + 0.3265306122 + x2 = 0 + 0.3265306122 Reorder the terms: -0.3265306122 + 0.3265306122 + -0.02040816327x + x2 = 0 + 0.3265306122 Combine like terms: -0.3265306122 + 0.3265306122 = 0.0000000000 0.0000000000 + -0.02040816327x + x2 = 0 + 0.3265306122 -0.02040816327x + x2 = 0 + 0.3265306122 Combine like terms: 0 + 0.3265306122 = 0.3265306122 -0.02040816327x + x2 = 0.3265306122 The x term is x. 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. -0.02040816327x + 0.25 + x2 = 0.3265306122 + 0.25 Reorder the terms: 0.25 + -0.02040816327x + x2 = 0.3265306122 + 0.25 Combine like terms: 0.3265306122 + 0.25 = 0.5765306122 0.25 + -0.02040816327x + x2 = 0.5765306122 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.5765306122 Calculate the square root of the right side: 0.759296129 Break this problem into two subproblems by setting (x + 0.5) equal to 0.759296129 and -0.759296129.Subproblem 1
x + 0.5 = 0.759296129 Simplifying x + 0.5 = 0.759296129 Reorder the terms: 0.5 + x = 0.759296129 Solving 0.5 + x = 0.759296129 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 = 0.759296129 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.759296129 + -0.5 x = 0.759296129 + -0.5 Combine like terms: 0.759296129 + -0.5 = 0.259296129 x = 0.259296129 Simplifying x = 0.259296129Subproblem 2
x + 0.5 = -0.759296129 Simplifying x + 0.5 = -0.759296129 Reorder the terms: 0.5 + x = -0.759296129 Solving 0.5 + x = -0.759296129 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 = -0.759296129 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.759296129 + -0.5 x = -0.759296129 + -0.5 Combine like terms: -0.759296129 + -0.5 = -1.259296129 x = -1.259296129 Simplifying x = -1.259296129Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.259296129, -1.259296129}
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