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Simplifying x2 + 71x + 30 = 0 Reorder the terms: 30 + 71x + x2 = 0 Solving 30 + 71x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 71x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 71x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 71x + x2 = 0 + -30 71x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 71x + x2 = -30 The x term is 71x. Take half its coefficient (35.5). Square it (1260.25) and add it to both sides. Add '1260.25' to each side of the equation. 71x + 1260.25 + x2 = -30 + 1260.25 Reorder the terms: 1260.25 + 71x + x2 = -30 + 1260.25 Combine like terms: -30 + 1260.25 = 1230.25 1260.25 + 71x + x2 = 1230.25 Factor a perfect square on the left side: (x + 35.5)(x + 35.5) = 1230.25 Calculate the square root of the right side: 35.074919815 Break this problem into two subproblems by setting (x + 35.5) equal to 35.074919815 and -35.074919815.Subproblem 1
x + 35.5 = 35.074919815 Simplifying x + 35.5 = 35.074919815 Reorder the terms: 35.5 + x = 35.074919815 Solving 35.5 + x = 35.074919815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.5' to each side of the equation. 35.5 + -35.5 + x = 35.074919815 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + x = 35.074919815 + -35.5 x = 35.074919815 + -35.5 Combine like terms: 35.074919815 + -35.5 = -0.425080185 x = -0.425080185 Simplifying x = -0.425080185Subproblem 2
x + 35.5 = -35.074919815 Simplifying x + 35.5 = -35.074919815 Reorder the terms: 35.5 + x = -35.074919815 Solving 35.5 + x = -35.074919815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35.5' to each side of the equation. 35.5 + -35.5 + x = -35.074919815 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + x = -35.074919815 + -35.5 x = -35.074919815 + -35.5 Combine like terms: -35.074919815 + -35.5 = -70.574919815 x = -70.574919815 Simplifying x = -70.574919815Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.425080185, -70.574919815}
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