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Simplifying x2 + 15x + -44 = 0 Reorder the terms: -44 + 15x + x2 = 0 Solving -44 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 15x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + 15x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 15x + x2 = 0 + 44 15x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 15x + x2 = 44 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 44 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 44 + 56.25 Combine like terms: 44 + 56.25 = 100.25 56.25 + 15x + x2 = 100.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + 7.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + 7.5 = 10.012492197 Simplifying x + 7.5 = 10.012492197 Reorder the terms: 7.5 + x = 10.012492197 Solving 7.5 + x = 10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 10.012492197 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 10.012492197 + -7.5 x = 10.012492197 + -7.5 Combine like terms: 10.012492197 + -7.5 = 2.512492197 x = 2.512492197 Simplifying x = 2.512492197Subproblem 2
x + 7.5 = -10.012492197 Simplifying x + 7.5 = -10.012492197 Reorder the terms: 7.5 + x = -10.012492197 Solving 7.5 + x = -10.012492197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -10.012492197 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -10.012492197 + -7.5 x = -10.012492197 + -7.5 Combine like terms: -10.012492197 + -7.5 = -17.512492197 x = -17.512492197 Simplifying x = -17.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.512492197, -17.512492197}
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