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Simplifying x2 + 20x + -350 = 0 Reorder the terms: -350 + 20x + x2 = 0 Solving -350 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '350' to each side of the equation. -350 + 20x + 350 + x2 = 0 + 350 Reorder the terms: -350 + 350 + 20x + x2 = 0 + 350 Combine like terms: -350 + 350 = 0 0 + 20x + x2 = 0 + 350 20x + x2 = 0 + 350 Combine like terms: 0 + 350 = 350 20x + x2 = 350 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 350 + 100 Reorder the terms: 100 + 20x + x2 = 350 + 100 Combine like terms: 350 + 100 = 450 100 + 20x + x2 = 450 Factor a perfect square on the left side: (x + 10)(x + 10) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (x + 10) equal to 21.213203436 and -21.213203436.Subproblem 1
x + 10 = 21.213203436 Simplifying x + 10 = 21.213203436 Reorder the terms: 10 + x = 21.213203436 Solving 10 + x = 21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 21.213203436 + -10 Combine like terms: 10 + -10 = 0 0 + x = 21.213203436 + -10 x = 21.213203436 + -10 Combine like terms: 21.213203436 + -10 = 11.213203436 x = 11.213203436 Simplifying x = 11.213203436Subproblem 2
x + 10 = -21.213203436 Simplifying x + 10 = -21.213203436 Reorder the terms: 10 + x = -21.213203436 Solving 10 + x = -21.213203436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -21.213203436 + -10 Combine like terms: 10 + -10 = 0 0 + x = -21.213203436 + -10 x = -21.213203436 + -10 Combine like terms: -21.213203436 + -10 = -31.213203436 x = -31.213203436 Simplifying x = -31.213203436Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.213203436, -31.213203436}
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