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Simplifying x2 + 35x + 7 = 0 Reorder the terms: 7 + 35x + x2 = 0 Solving 7 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 35x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 35x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 35x + x2 = 0 + -7 35x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 35x + x2 = -7 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 = -7 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -7 + 306.25 Combine like terms: -7 + 306.25 = 299.25 306.25 + 35x + x2 = 299.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 299.25 Calculate the square root of the right side: 17.298843892 Break this problem into two subproblems by setting (x + 17.5) equal to 17.298843892 and -17.298843892.Subproblem 1
x + 17.5 = 17.298843892 Simplifying x + 17.5 = 17.298843892 Reorder the terms: 17.5 + x = 17.298843892 Solving 17.5 + x = 17.298843892 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 = 17.298843892 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 17.298843892 + -17.5 x = 17.298843892 + -17.5 Combine like terms: 17.298843892 + -17.5 = -0.201156108 x = -0.201156108 Simplifying x = -0.201156108Subproblem 2
x + 17.5 = -17.298843892 Simplifying x + 17.5 = -17.298843892 Reorder the terms: 17.5 + x = -17.298843892 Solving 17.5 + x = -17.298843892 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 = -17.298843892 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -17.298843892 + -17.5 x = -17.298843892 + -17.5 Combine like terms: -17.298843892 + -17.5 = -34.798843892 x = -34.798843892 Simplifying x = -34.798843892Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.201156108, -34.798843892}
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