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Simplifying x2 + -7x + -68 = 0 Reorder the terms: -68 + -7x + x2 = 0 Solving -68 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + -7x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + -7x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + -7x + x2 = 0 + 68 -7x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 -7x + x2 = 68 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 68 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 68 + 12.25 Combine like terms: 68 + 12.25 = 80.25 12.25 + -7x + x2 = 80.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (x + -3.5) equal to 8.958236434 and -8.958236434.Subproblem 1
x + -3.5 = 8.958236434 Simplifying x + -3.5 = 8.958236434 Reorder the terms: -3.5 + x = 8.958236434 Solving -3.5 + x = 8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 8.958236434 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 8.958236434 + 3.5 x = 8.958236434 + 3.5 Combine like terms: 8.958236434 + 3.5 = 12.458236434 x = 12.458236434 Simplifying x = 12.458236434Subproblem 2
x + -3.5 = -8.958236434 Simplifying x + -3.5 = -8.958236434 Reorder the terms: -3.5 + x = -8.958236434 Solving -3.5 + x = -8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -8.958236434 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -8.958236434 + 3.5 x = -8.958236434 + 3.5 Combine like terms: -8.958236434 + 3.5 = -5.458236434 x = -5.458236434 Simplifying x = -5.458236434Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.458236434, -5.458236434}
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