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Simplifying x2 + -10x + -894 = 0 Reorder the terms: -894 + -10x + x2 = 0 Solving -894 + -10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '894' to each side of the equation. -894 + -10x + 894 + x2 = 0 + 894 Reorder the terms: -894 + 894 + -10x + x2 = 0 + 894 Combine like terms: -894 + 894 = 0 0 + -10x + x2 = 0 + 894 -10x + x2 = 0 + 894 Combine like terms: 0 + 894 = 894 -10x + x2 = 894 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 894 + 25 Reorder the terms: 25 + -10x + x2 = 894 + 25 Combine like terms: 894 + 25 = 919 25 + -10x + x2 = 919 Factor a perfect square on the left side: (x + -5)(x + -5) = 919 Calculate the square root of the right side: 30.315012782 Break this problem into two subproblems by setting (x + -5) equal to 30.315012782 and -30.315012782.Subproblem 1
x + -5 = 30.315012782 Simplifying x + -5 = 30.315012782 Reorder the terms: -5 + x = 30.315012782 Solving -5 + x = 30.315012782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 30.315012782 + 5 Combine like terms: -5 + 5 = 0 0 + x = 30.315012782 + 5 x = 30.315012782 + 5 Combine like terms: 30.315012782 + 5 = 35.315012782 x = 35.315012782 Simplifying x = 35.315012782Subproblem 2
x + -5 = -30.315012782 Simplifying x + -5 = -30.315012782 Reorder the terms: -5 + x = -30.315012782 Solving -5 + x = -30.315012782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -30.315012782 + 5 Combine like terms: -5 + 5 = 0 0 + x = -30.315012782 + 5 x = -30.315012782 + 5 Combine like terms: -30.315012782 + 5 = -25.315012782 x = -25.315012782 Simplifying x = -25.315012782Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.315012782, -25.315012782}
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