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Simplifying x2 + 35x + 29 = 0 Reorder the terms: 29 + 35x + x2 = 0 Solving 29 + 35x + 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 + 35x + -29 + x2 = 0 + -29 Reorder the terms: 29 + -29 + 35x + x2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 35x + x2 = 0 + -29 35x + x2 = 0 + -29 Combine like terms: 0 + -29 = -29 35x + x2 = -29 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = -29 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -29 + 306.25 Combine like terms: -29 + 306.25 = 277.25 306.25 + 35x + x2 = 277.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 277.25 Calculate the square root of the right side: 16.650825805 Break this problem into two subproblems by setting (x + 17.5) equal to 16.650825805 and -16.650825805.Subproblem 1
x + 17.5 = 16.650825805 Simplifying x + 17.5 = 16.650825805 Reorder the terms: 17.5 + x = 16.650825805 Solving 17.5 + x = 16.650825805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 16.650825805 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 16.650825805 + -17.5 x = 16.650825805 + -17.5 Combine like terms: 16.650825805 + -17.5 = -0.849174195 x = -0.849174195 Simplifying x = -0.849174195Subproblem 2
x + 17.5 = -16.650825805 Simplifying x + 17.5 = -16.650825805 Reorder the terms: 17.5 + x = -16.650825805 Solving 17.5 + x = -16.650825805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -16.650825805 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -16.650825805 + -17.5 x = -16.650825805 + -17.5 Combine like terms: -16.650825805 + -17.5 = -34.150825805 x = -34.150825805 Simplifying x = -34.150825805Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.849174195, -34.150825805}
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