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Simplifying x2 + 35x + -72 = 0 Reorder the terms: -72 + 35x + x2 = 0 Solving -72 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + 35x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 35x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 35x + x2 = 0 + 72 35x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 35x + x2 = 72 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 = 72 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 72 + 306.25 Combine like terms: 72 + 306.25 = 378.25 306.25 + 35x + x2 = 378.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 378.25 Calculate the square root of the right side: 19.448650339 Break this problem into two subproblems by setting (x + 17.5) equal to 19.448650339 and -19.448650339.Subproblem 1
x + 17.5 = 19.448650339 Simplifying x + 17.5 = 19.448650339 Reorder the terms: 17.5 + x = 19.448650339 Solving 17.5 + x = 19.448650339 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 = 19.448650339 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 19.448650339 + -17.5 x = 19.448650339 + -17.5 Combine like terms: 19.448650339 + -17.5 = 1.948650339 x = 1.948650339 Simplifying x = 1.948650339Subproblem 2
x + 17.5 = -19.448650339 Simplifying x + 17.5 = -19.448650339 Reorder the terms: 17.5 + x = -19.448650339 Solving 17.5 + x = -19.448650339 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 = -19.448650339 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -19.448650339 + -17.5 x = -19.448650339 + -17.5 Combine like terms: -19.448650339 + -17.5 = -36.948650339 x = -36.948650339 Simplifying x = -36.948650339Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.948650339, -36.948650339}
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