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Simplifying x2 + 10x + -96 = 6 Reorder the terms: -96 + 10x + x2 = 6 Solving -96 + 10x + x2 = 6 Solving for variable 'x'. Reorder the terms: -96 + -6 + 10x + x2 = 6 + -6 Combine like terms: -96 + -6 = -102 -102 + 10x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -102 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '102' to each side of the equation. -102 + 10x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + 10x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + 10x + x2 = 0 + 102 10x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 10x + x2 = 102 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 = 102 + 25 Reorder the terms: 25 + 10x + x2 = 102 + 25 Combine like terms: 102 + 25 = 127 25 + 10x + x2 = 127 Factor a perfect square on the left side: (x + 5)(x + 5) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (x + 5) equal to 11.26942767 and -11.26942767.Subproblem 1
x + 5 = 11.26942767 Simplifying x + 5 = 11.26942767 Reorder the terms: 5 + x = 11.26942767 Solving 5 + x = 11.26942767 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 = 11.26942767 + -5 Combine like terms: 5 + -5 = 0 0 + x = 11.26942767 + -5 x = 11.26942767 + -5 Combine like terms: 11.26942767 + -5 = 6.26942767 x = 6.26942767 Simplifying x = 6.26942767Subproblem 2
x + 5 = -11.26942767 Simplifying x + 5 = -11.26942767 Reorder the terms: 5 + x = -11.26942767 Solving 5 + x = -11.26942767 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 = -11.26942767 + -5 Combine like terms: 5 + -5 = 0 0 + x = -11.26942767 + -5 x = -11.26942767 + -5 Combine like terms: -11.26942767 + -5 = -16.26942767 x = -16.26942767 Simplifying x = -16.26942767Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.26942767, -16.26942767}
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