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Simplifying x2 + 14x = -6 Reorder the terms: 14x + x2 = -6 Solving 14x + x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + 14x + x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 14x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 14x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 14x + x2 = 0 + -6 14x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 14x + x2 = -6 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 = -6 + 49 Reorder the terms: 49 + 14x + x2 = -6 + 49 Combine like terms: -6 + 49 = 43 49 + 14x + x2 = 43 Factor a perfect square on the left side: (x + 7)(x + 7) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + 7) equal to 6.557438524 and -6.557438524.Subproblem 1
x + 7 = 6.557438524 Simplifying x + 7 = 6.557438524 Reorder the terms: 7 + x = 6.557438524 Solving 7 + x = 6.557438524 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 = 6.557438524 + -7 Combine like terms: 7 + -7 = 0 0 + x = 6.557438524 + -7 x = 6.557438524 + -7 Combine like terms: 6.557438524 + -7 = -0.442561476 x = -0.442561476 Simplifying x = -0.442561476Subproblem 2
x + 7 = -6.557438524 Simplifying x + 7 = -6.557438524 Reorder the terms: 7 + x = -6.557438524 Solving 7 + x = -6.557438524 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 = -6.557438524 + -7 Combine like terms: 7 + -7 = 0 0 + x = -6.557438524 + -7 x = -6.557438524 + -7 Combine like terms: -6.557438524 + -7 = -13.557438524 x = -13.557438524 Simplifying x = -13.557438524Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.442561476, -13.557438524}
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