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Simplifying x2 + 14x + -29 = 0 Reorder the terms: -29 + 14x + x2 = 0 Solving -29 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 14x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 14x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 14x + x2 = 0 + 29 14x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 14x + x2 = 29 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 = 29 + 49 Reorder the terms: 49 + 14x + x2 = 29 + 49 Combine like terms: 29 + 49 = 78 49 + 14x + x2 = 78 Factor a perfect square on the left side: (x + 7)(x + 7) = 78 Calculate the square root of the right side: 8.831760866 Break this problem into two subproblems by setting (x + 7) equal to 8.831760866 and -8.831760866.Subproblem 1
x + 7 = 8.831760866 Simplifying x + 7 = 8.831760866 Reorder the terms: 7 + x = 8.831760866 Solving 7 + x = 8.831760866 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 = 8.831760866 + -7 Combine like terms: 7 + -7 = 0 0 + x = 8.831760866 + -7 x = 8.831760866 + -7 Combine like terms: 8.831760866 + -7 = 1.831760866 x = 1.831760866 Simplifying x = 1.831760866Subproblem 2
x + 7 = -8.831760866 Simplifying x + 7 = -8.831760866 Reorder the terms: 7 + x = -8.831760866 Solving 7 + x = -8.831760866 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 = -8.831760866 + -7 Combine like terms: 7 + -7 = 0 0 + x = -8.831760866 + -7 x = -8.831760866 + -7 Combine like terms: -8.831760866 + -7 = -15.831760866 x = -15.831760866 Simplifying x = -15.831760866Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.831760866, -15.831760866}
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