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Simplifying x2 + 20x + -56 = 3 Reorder the terms: -56 + 20x + x2 = 3 Solving -56 + 20x + x2 = 3 Solving for variable 'x'. Reorder the terms: -56 + -3 + 20x + x2 = 3 + -3 Combine like terms: -56 + -3 = -59 -59 + 20x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -59 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + 20x + 59 + x2 = 0 + 59 Reorder the terms: -59 + 59 + 20x + x2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + 20x + x2 = 0 + 59 20x + x2 = 0 + 59 Combine like terms: 0 + 59 = 59 20x + x2 = 59 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 = 59 + 100 Reorder the terms: 100 + 20x + x2 = 59 + 100 Combine like terms: 59 + 100 = 159 100 + 20x + x2 = 159 Factor a perfect square on the left side: (x + 10)(x + 10) = 159 Calculate the square root of the right side: 12.609520213 Break this problem into two subproblems by setting (x + 10) equal to 12.609520213 and -12.609520213.Subproblem 1
x + 10 = 12.609520213 Simplifying x + 10 = 12.609520213 Reorder the terms: 10 + x = 12.609520213 Solving 10 + x = 12.609520213 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 = 12.609520213 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.609520213 + -10 x = 12.609520213 + -10 Combine like terms: 12.609520213 + -10 = 2.609520213 x = 2.609520213 Simplifying x = 2.609520213Subproblem 2
x + 10 = -12.609520213 Simplifying x + 10 = -12.609520213 Reorder the terms: 10 + x = -12.609520213 Solving 10 + x = -12.609520213 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 = -12.609520213 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.609520213 + -10 x = -12.609520213 + -10 Combine like terms: -12.609520213 + -10 = -22.609520213 x = -22.609520213 Simplifying x = -22.609520213Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.609520213, -22.609520213}
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