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Simplifying 1x2 + 50x = 30 Reorder the terms: 50x + 1x2 = 30 Solving 50x + 1x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 50x + 1x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 50x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 50x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 50x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 50x + x2 = 0 + 30 50x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 50x + x2 = 30 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 = 30 + 625 Reorder the terms: 625 + 50x + x2 = 30 + 625 Combine like terms: 30 + 625 = 655 625 + 50x + x2 = 655 Factor a perfect square on the left side: (x + 25)(x + 25) = 655 Calculate the square root of the right side: 25.592967784 Break this problem into two subproblems by setting (x + 25) equal to 25.592967784 and -25.592967784.Subproblem 1
x + 25 = 25.592967784 Simplifying x + 25 = 25.592967784 Reorder the terms: 25 + x = 25.592967784 Solving 25 + x = 25.592967784 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 = 25.592967784 + -25 Combine like terms: 25 + -25 = 0 0 + x = 25.592967784 + -25 x = 25.592967784 + -25 Combine like terms: 25.592967784 + -25 = 0.592967784 x = 0.592967784 Simplifying x = 0.592967784Subproblem 2
x + 25 = -25.592967784 Simplifying x + 25 = -25.592967784 Reorder the terms: 25 + x = -25.592967784 Solving 25 + x = -25.592967784 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 = -25.592967784 + -25 Combine like terms: 25 + -25 = 0 0 + x = -25.592967784 + -25 x = -25.592967784 + -25 Combine like terms: -25.592967784 + -25 = -50.592967784 x = -50.592967784 Simplifying x = -50.592967784Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.592967784, -50.592967784}
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