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Simplifying x2 + 50x + -16 = 0 Reorder the terms: -16 + 50x + x2 = 0 Solving -16 + 50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 50x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 50x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 50x + x2 = 0 + 16 50x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 50x + x2 = 16 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 16 + 625 Reorder the terms: 625 + 50x + x2 = 16 + 625 Combine like terms: 16 + 625 = 641 625 + 50x + x2 = 641 Factor a perfect square on the left side: (x + 25)(x + 25) = 641 Calculate the square root of the right side: 25.317977802 Break this problem into two subproblems by setting (x + 25) equal to 25.317977802 and -25.317977802.Subproblem 1
x + 25 = 25.317977802 Simplifying x + 25 = 25.317977802 Reorder the terms: 25 + x = 25.317977802 Solving 25 + x = 25.317977802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 25.317977802 + -25 Combine like terms: 25 + -25 = 0 0 + x = 25.317977802 + -25 x = 25.317977802 + -25 Combine like terms: 25.317977802 + -25 = 0.317977802 x = 0.317977802 Simplifying x = 0.317977802Subproblem 2
x + 25 = -25.317977802 Simplifying x + 25 = -25.317977802 Reorder the terms: 25 + x = -25.317977802 Solving 25 + x = -25.317977802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -25.317977802 + -25 Combine like terms: 25 + -25 = 0 0 + x = -25.317977802 + -25 x = -25.317977802 + -25 Combine like terms: -25.317977802 + -25 = -50.317977802 x = -50.317977802 Simplifying x = -50.317977802Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.317977802, -50.317977802}
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