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Simplifying 1 + -2x(x + 50) = 0 Reorder the terms: 1 + -2x(50 + x) = 0 1 + (50 * -2x + x * -2x) = 0 1 + (-100x + -2x2) = 0 Solving 1 + -100x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + 50x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 50x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 50x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 50x + x2 = 0 + 0.5 50x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 50x + x2 = 0.5 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 = 0.5 + 625 Reorder the terms: 625 + 50x + x2 = 0.5 + 625 Combine like terms: 0.5 + 625 = 625.5 625 + 50x + x2 = 625.5 Factor a perfect square on the left side: (x + 25)(x + 25) = 625.5 Calculate the square root of the right side: 25.009998001 Break this problem into two subproblems by setting (x + 25) equal to 25.009998001 and -25.009998001.Subproblem 1
x + 25 = 25.009998001 Simplifying x + 25 = 25.009998001 Reorder the terms: 25 + x = 25.009998001 Solving 25 + x = 25.009998001 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 = 25.009998001 + -25 Combine like terms: 25 + -25 = 0 0 + x = 25.009998001 + -25 x = 25.009998001 + -25 Combine like terms: 25.009998001 + -25 = 0.009998001 x = 0.009998001 Simplifying x = 0.009998001Subproblem 2
x + 25 = -25.009998001 Simplifying x + 25 = -25.009998001 Reorder the terms: 25 + x = -25.009998001 Solving 25 + x = -25.009998001 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 = -25.009998001 + -25 Combine like terms: 25 + -25 = 0 0 + x = -25.009998001 + -25 x = -25.009998001 + -25 Combine like terms: -25.009998001 + -25 = -50.009998001 x = -50.009998001 Simplifying x = -50.009998001Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.009998001, -50.009998001}
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