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Simplifying x(x) + 14x = -2 Multiply x * x x2 + 14x = -2 Reorder the terms: 14x + x2 = -2 Solving 14x + x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 14x + x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 14x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 14x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 14x + x2 = 0 + -2 14x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 14x + x2 = -2 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 = -2 + 49 Reorder the terms: 49 + 14x + x2 = -2 + 49 Combine like terms: -2 + 49 = 47 49 + 14x + x2 = 47 Factor a perfect square on the left side: (x + 7)(x + 7) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + 7) equal to 6.8556546 and -6.8556546.Subproblem 1
x + 7 = 6.8556546 Simplifying x + 7 = 6.8556546 Reorder the terms: 7 + x = 6.8556546 Solving 7 + x = 6.8556546 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 = 6.8556546 + -7 Combine like terms: 7 + -7 = 0 0 + x = 6.8556546 + -7 x = 6.8556546 + -7 Combine like terms: 6.8556546 + -7 = -0.1443454 x = -0.1443454 Simplifying x = -0.1443454Subproblem 2
x + 7 = -6.8556546 Simplifying x + 7 = -6.8556546 Reorder the terms: 7 + x = -6.8556546 Solving 7 + x = -6.8556546 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 = -6.8556546 + -7 Combine like terms: 7 + -7 = 0 0 + x = -6.8556546 + -7 x = -6.8556546 + -7 Combine like terms: -6.8556546 + -7 = -13.8556546 x = -13.8556546 Simplifying x = -13.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1443454, -13.8556546}
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