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Simplifying x2 + 20x + -450 = 0 Reorder the terms: -450 + 20x + x2 = 0 Solving -450 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '450' to each side of the equation. -450 + 20x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + 20x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 20x + x2 = 0 + 450 20x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 20x + x2 = 450 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 = 450 + 100 Reorder the terms: 100 + 20x + x2 = 450 + 100 Combine like terms: 450 + 100 = 550 100 + 20x + x2 = 550 Factor a perfect square on the left side: (x + 10)(x + 10) = 550 Calculate the square root of the right side: 23.452078799 Break this problem into two subproblems by setting (x + 10) equal to 23.452078799 and -23.452078799.Subproblem 1
x + 10 = 23.452078799 Simplifying x + 10 = 23.452078799 Reorder the terms: 10 + x = 23.452078799 Solving 10 + x = 23.452078799 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 = 23.452078799 + -10 Combine like terms: 10 + -10 = 0 0 + x = 23.452078799 + -10 x = 23.452078799 + -10 Combine like terms: 23.452078799 + -10 = 13.452078799 x = 13.452078799 Simplifying x = 13.452078799Subproblem 2
x + 10 = -23.452078799 Simplifying x + 10 = -23.452078799 Reorder the terms: 10 + x = -23.452078799 Solving 10 + x = -23.452078799 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 = -23.452078799 + -10 Combine like terms: 10 + -10 = 0 0 + x = -23.452078799 + -10 x = -23.452078799 + -10 Combine like terms: -23.452078799 + -10 = -33.452078799 x = -33.452078799 Simplifying x = -33.452078799Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.452078799, -33.452078799}
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