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Simplifying x2 + 39x + -50 = 0 Reorder the terms: -50 + 39x + x2 = 0 Solving -50 + 39x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 39x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 39x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 39x + x2 = 0 + 50 39x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 39x + x2 = 50 The x term is 39x. Take half its coefficient (19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. 39x + 380.25 + x2 = 50 + 380.25 Reorder the terms: 380.25 + 39x + x2 = 50 + 380.25 Combine like terms: 50 + 380.25 = 430.25 380.25 + 39x + x2 = 430.25 Factor a perfect square on the left side: (x + 19.5)(x + 19.5) = 430.25 Calculate the square root of the right side: 20.742468513 Break this problem into two subproblems by setting (x + 19.5) equal to 20.742468513 and -20.742468513.Subproblem 1
x + 19.5 = 20.742468513 Simplifying x + 19.5 = 20.742468513 Reorder the terms: 19.5 + x = 20.742468513 Solving 19.5 + x = 20.742468513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = 20.742468513 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = 20.742468513 + -19.5 x = 20.742468513 + -19.5 Combine like terms: 20.742468513 + -19.5 = 1.242468513 x = 1.242468513 Simplifying x = 1.242468513Subproblem 2
x + 19.5 = -20.742468513 Simplifying x + 19.5 = -20.742468513 Reorder the terms: 19.5 + x = -20.742468513 Solving 19.5 + x = -20.742468513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.5' to each side of the equation. 19.5 + -19.5 + x = -20.742468513 + -19.5 Combine like terms: 19.5 + -19.5 = 0.0 0.0 + x = -20.742468513 + -19.5 x = -20.742468513 + -19.5 Combine like terms: -20.742468513 + -19.5 = -40.242468513 x = -40.242468513 Simplifying x = -40.242468513Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.242468513, -40.242468513}
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