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Simplifying x2 + 20x + -73 = 0 Reorder the terms: -73 + 20x + x2 = 0 Solving -73 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + 20x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + 20x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + 20x + x2 = 0 + 73 20x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 20x + x2 = 73 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 = 73 + 100 Reorder the terms: 100 + 20x + x2 = 73 + 100 Combine like terms: 73 + 100 = 173 100 + 20x + x2 = 173 Factor a perfect square on the left side: (x + 10)(x + 10) = 173 Calculate the square root of the right side: 13.152946438 Break this problem into two subproblems by setting (x + 10) equal to 13.152946438 and -13.152946438.Subproblem 1
x + 10 = 13.152946438 Simplifying x + 10 = 13.152946438 Reorder the terms: 10 + x = 13.152946438 Solving 10 + x = 13.152946438 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 = 13.152946438 + -10 Combine like terms: 10 + -10 = 0 0 + x = 13.152946438 + -10 x = 13.152946438 + -10 Combine like terms: 13.152946438 + -10 = 3.152946438 x = 3.152946438 Simplifying x = 3.152946438Subproblem 2
x + 10 = -13.152946438 Simplifying x + 10 = -13.152946438 Reorder the terms: 10 + x = -13.152946438 Solving 10 + x = -13.152946438 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 = -13.152946438 + -10 Combine like terms: 10 + -10 = 0 0 + x = -13.152946438 + -10 x = -13.152946438 + -10 Combine like terms: -13.152946438 + -10 = -23.152946438 x = -23.152946438 Simplifying x = -23.152946438Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.152946438, -23.152946438}
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