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Simplifying x2 + -20x + -56 = 0 Reorder the terms: -56 + -20x + x2 = 0 Solving -56 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -20x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -20x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -20x + x2 = 0 + 56 -20x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -20x + x2 = 56 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 = 56 + 100 Reorder the terms: 100 + -20x + x2 = 56 + 100 Combine like terms: 56 + 100 = 156 100 + -20x + x2 = 156 Factor a perfect square on the left side: (x + -10)(x + -10) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + -10) equal to 12.489995997 and -12.489995997.Subproblem 1
x + -10 = 12.489995997 Simplifying x + -10 = 12.489995997 Reorder the terms: -10 + x = 12.489995997 Solving -10 + x = 12.489995997 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 = 12.489995997 + 10 Combine like terms: -10 + 10 = 0 0 + x = 12.489995997 + 10 x = 12.489995997 + 10 Combine like terms: 12.489995997 + 10 = 22.489995997 x = 22.489995997 Simplifying x = 22.489995997Subproblem 2
x + -10 = -12.489995997 Simplifying x + -10 = -12.489995997 Reorder the terms: -10 + x = -12.489995997 Solving -10 + x = -12.489995997 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 = -12.489995997 + 10 Combine like terms: -10 + 10 = 0 0 + x = -12.489995997 + 10 x = -12.489995997 + 10 Combine like terms: -12.489995997 + 10 = -2.489995997 x = -2.489995997 Simplifying x = -2.489995997Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.489995997, -2.489995997}
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