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Simplifying x2 + -20x + -46 = -4 Reorder the terms: -46 + -20x + x2 = -4 Solving -46 + -20x + x2 = -4 Solving for variable 'x'. Reorder the terms: -46 + 4 + -20x + x2 = -4 + 4 Combine like terms: -46 + 4 = -42 -42 + -20x + x2 = -4 + 4 Combine like terms: -4 + 4 = 0 -42 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -20x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -20x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -20x + x2 = 0 + 42 -20x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -20x + x2 = 42 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 = 42 + 100 Reorder the terms: 100 + -20x + x2 = 42 + 100 Combine like terms: 42 + 100 = 142 100 + -20x + x2 = 142 Factor a perfect square on the left side: (x + -10)(x + -10) = 142 Calculate the square root of the right side: 11.916375288 Break this problem into two subproblems by setting (x + -10) equal to 11.916375288 and -11.916375288.Subproblem 1
x + -10 = 11.916375288 Simplifying x + -10 = 11.916375288 Reorder the terms: -10 + x = 11.916375288 Solving -10 + x = 11.916375288 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 = 11.916375288 + 10 Combine like terms: -10 + 10 = 0 0 + x = 11.916375288 + 10 x = 11.916375288 + 10 Combine like terms: 11.916375288 + 10 = 21.916375288 x = 21.916375288 Simplifying x = 21.916375288Subproblem 2
x + -10 = -11.916375288 Simplifying x + -10 = -11.916375288 Reorder the terms: -10 + x = -11.916375288 Solving -10 + x = -11.916375288 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 = -11.916375288 + 10 Combine like terms: -10 + 10 = 0 0 + x = -11.916375288 + 10 x = -11.916375288 + 10 Combine like terms: -11.916375288 + 10 = -1.916375288 x = -1.916375288 Simplifying x = -1.916375288Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.916375288, -1.916375288}
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