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Simplifying x2 + 10x + -68 = 0 Reorder the terms: -68 + 10x + x2 = 0 Solving -68 + 10x + 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 + 10x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + 10x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + 10x + x2 = 0 + 68 10x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 10x + x2 = 68 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 = 68 + 25 Reorder the terms: 25 + 10x + x2 = 68 + 25 Combine like terms: 68 + 25 = 93 25 + 10x + x2 = 93 Factor a perfect square on the left side: (x + 5)(x + 5) = 93 Calculate the square root of the right side: 9.643650761 Break this problem into two subproblems by setting (x + 5) equal to 9.643650761 and -9.643650761.Subproblem 1
x + 5 = 9.643650761 Simplifying x + 5 = 9.643650761 Reorder the terms: 5 + x = 9.643650761 Solving 5 + x = 9.643650761 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 = 9.643650761 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.643650761 + -5 x = 9.643650761 + -5 Combine like terms: 9.643650761 + -5 = 4.643650761 x = 4.643650761 Simplifying x = 4.643650761Subproblem 2
x + 5 = -9.643650761 Simplifying x + 5 = -9.643650761 Reorder the terms: 5 + x = -9.643650761 Solving 5 + x = -9.643650761 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 = -9.643650761 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.643650761 + -5 x = -9.643650761 + -5 Combine like terms: -9.643650761 + -5 = -14.643650761 x = -14.643650761 Simplifying x = -14.643650761Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.643650761, -14.643650761}
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