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Simplifying x2 + -10x + -51 = 4 Reorder the terms: -51 + -10x + x2 = 4 Solving -51 + -10x + x2 = 4 Solving for variable 'x'. Reorder the terms: -51 + -4 + -10x + x2 = 4 + -4 Combine like terms: -51 + -4 = -55 -55 + -10x + x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -55 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + -10x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + -10x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -10x + x2 = 0 + 55 -10x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 -10x + x2 = 55 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 = 55 + 25 Reorder the terms: 25 + -10x + x2 = 55 + 25 Combine like terms: 55 + 25 = 80 25 + -10x + x2 = 80 Factor a perfect square on the left side: (x + -5)(x + -5) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -5) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -5 = 8.94427191 Simplifying x + -5 = 8.94427191 Reorder the terms: -5 + x = 8.94427191 Solving -5 + x = 8.94427191 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 = 8.94427191 + 5 Combine like terms: -5 + 5 = 0 0 + x = 8.94427191 + 5 x = 8.94427191 + 5 Combine like terms: 8.94427191 + 5 = 13.94427191 x = 13.94427191 Simplifying x = 13.94427191Subproblem 2
x + -5 = -8.94427191 Simplifying x + -5 = -8.94427191 Reorder the terms: -5 + x = -8.94427191 Solving -5 + x = -8.94427191 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 = -8.94427191 + 5 Combine like terms: -5 + 5 = 0 0 + x = -8.94427191 + 5 x = -8.94427191 + 5 Combine like terms: -8.94427191 + 5 = -3.94427191 x = -3.94427191 Simplifying x = -3.94427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.94427191, -3.94427191}
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