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Simplifying x2 + 14x + -11 = 0 Reorder the terms: -11 + 14x + x2 = 0 Solving -11 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 14x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 14x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 14x + x2 = 0 + 11 14x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 14x + x2 = 11 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 11 + 49 Reorder the terms: 49 + 14x + x2 = 11 + 49 Combine like terms: 11 + 49 = 60 49 + 14x + x2 = 60 Factor a perfect square on the left side: (x + 7)(x + 7) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + 7) equal to 7.745966692 and -7.745966692.Subproblem 1
x + 7 = 7.745966692 Simplifying x + 7 = 7.745966692 Reorder the terms: 7 + x = 7.745966692 Solving 7 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 7.745966692 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.745966692 + -7 x = 7.745966692 + -7 Combine like terms: 7.745966692 + -7 = 0.745966692 x = 0.745966692 Simplifying x = 0.745966692Subproblem 2
x + 7 = -7.745966692 Simplifying x + 7 = -7.745966692 Reorder the terms: 7 + x = -7.745966692 Solving 7 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -7.745966692 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.745966692 + -7 x = -7.745966692 + -7 Combine like terms: -7.745966692 + -7 = -14.745966692 x = -14.745966692 Simplifying x = -14.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.745966692, -14.745966692}
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