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Simplifying x2 + 29x + 79 = 0 Reorder the terms: 79 + 29x + x2 = 0 Solving 79 + 29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-79' to each side of the equation. 79 + 29x + -79 + x2 = 0 + -79 Reorder the terms: 79 + -79 + 29x + x2 = 0 + -79 Combine like terms: 79 + -79 = 0 0 + 29x + x2 = 0 + -79 29x + x2 = 0 + -79 Combine like terms: 0 + -79 = -79 29x + x2 = -79 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = -79 + 210.25 Reorder the terms: 210.25 + 29x + x2 = -79 + 210.25 Combine like terms: -79 + 210.25 = 131.25 210.25 + 29x + x2 = 131.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 131.25 Calculate the square root of the right side: 11.456439237 Break this problem into two subproblems by setting (x + 14.5) equal to 11.456439237 and -11.456439237.Subproblem 1
x + 14.5 = 11.456439237 Simplifying x + 14.5 = 11.456439237 Reorder the terms: 14.5 + x = 11.456439237 Solving 14.5 + x = 11.456439237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 11.456439237 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 11.456439237 + -14.5 x = 11.456439237 + -14.5 Combine like terms: 11.456439237 + -14.5 = -3.043560763 x = -3.043560763 Simplifying x = -3.043560763Subproblem 2
x + 14.5 = -11.456439237 Simplifying x + 14.5 = -11.456439237 Reorder the terms: 14.5 + x = -11.456439237 Solving 14.5 + x = -11.456439237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -11.456439237 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -11.456439237 + -14.5 x = -11.456439237 + -14.5 Combine like terms: -11.456439237 + -14.5 = -25.956439237 x = -25.956439237 Simplifying x = -25.956439237Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.043560763, -25.956439237}
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