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Simplifying x2 + 38x + 70 = 0 Reorder the terms: 70 + 38x + x2 = 0 Solving 70 + 38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + 38x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + 38x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + 38x + x2 = 0 + -70 38x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 38x + x2 = -70 The x term is 38x. Take half its coefficient (19). Square it (361) and add it to both sides. Add '361' to each side of the equation. 38x + 361 + x2 = -70 + 361 Reorder the terms: 361 + 38x + x2 = -70 + 361 Combine like terms: -70 + 361 = 291 361 + 38x + x2 = 291 Factor a perfect square on the left side: (x + 19)(x + 19) = 291 Calculate the square root of the right side: 17.058722109 Break this problem into two subproblems by setting (x + 19) equal to 17.058722109 and -17.058722109.Subproblem 1
x + 19 = 17.058722109 Simplifying x + 19 = 17.058722109 Reorder the terms: 19 + x = 17.058722109 Solving 19 + x = 17.058722109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 17.058722109 + -19 Combine like terms: 19 + -19 = 0 0 + x = 17.058722109 + -19 x = 17.058722109 + -19 Combine like terms: 17.058722109 + -19 = -1.941277891 x = -1.941277891 Simplifying x = -1.941277891Subproblem 2
x + 19 = -17.058722109 Simplifying x + 19 = -17.058722109 Reorder the terms: 19 + x = -17.058722109 Solving 19 + x = -17.058722109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = -17.058722109 + -19 Combine like terms: 19 + -19 = 0 0 + x = -17.058722109 + -19 x = -17.058722109 + -19 Combine like terms: -17.058722109 + -19 = -36.058722109 x = -36.058722109 Simplifying x = -36.058722109Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.941277891, -36.058722109}
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