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Simplifying x2 + 20x + -45 = 0 Reorder the terms: -45 + 20x + x2 = 0 Solving -45 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 20x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 20x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 20x + x2 = 0 + 45 20x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 20x + x2 = 45 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 = 45 + 100 Reorder the terms: 100 + 20x + x2 = 45 + 100 Combine like terms: 45 + 100 = 145 100 + 20x + x2 = 145 Factor a perfect square on the left side: (x + 10)(x + 10) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + 10) equal to 12.041594579 and -12.041594579.Subproblem 1
x + 10 = 12.041594579 Simplifying x + 10 = 12.041594579 Reorder the terms: 10 + x = 12.041594579 Solving 10 + x = 12.041594579 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 = 12.041594579 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.041594579 + -10 x = 12.041594579 + -10 Combine like terms: 12.041594579 + -10 = 2.041594579 x = 2.041594579 Simplifying x = 2.041594579Subproblem 2
x + 10 = -12.041594579 Simplifying x + 10 = -12.041594579 Reorder the terms: 10 + x = -12.041594579 Solving 10 + x = -12.041594579 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 = -12.041594579 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.041594579 + -10 x = -12.041594579 + -10 Combine like terms: -12.041594579 + -10 = -22.041594579 x = -22.041594579 Simplifying x = -22.041594579Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.041594579, -22.041594579}
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