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Simplifying x2 + 16x + -27 = 10 Reorder the terms: -27 + 16x + x2 = 10 Solving -27 + 16x + x2 = 10 Solving for variable 'x'. Reorder the terms: -27 + -10 + 16x + x2 = 10 + -10 Combine like terms: -27 + -10 = -37 -37 + 16x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -37 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 16x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + 16x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 16x + x2 = 0 + 37 16x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 16x + x2 = 37 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 37 + 64 Reorder the terms: 64 + 16x + x2 = 37 + 64 Combine like terms: 37 + 64 = 101 64 + 16x + x2 = 101 Factor a perfect square on the left side: (x + 8)(x + 8) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + 8) equal to 10.049875621 and -10.049875621.Subproblem 1
x + 8 = 10.049875621 Simplifying x + 8 = 10.049875621 Reorder the terms: 8 + x = 10.049875621 Solving 8 + x = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 10.049875621 + -8 Combine like terms: 8 + -8 = 0 0 + x = 10.049875621 + -8 x = 10.049875621 + -8 Combine like terms: 10.049875621 + -8 = 2.049875621 x = 2.049875621 Simplifying x = 2.049875621Subproblem 2
x + 8 = -10.049875621 Simplifying x + 8 = -10.049875621 Reorder the terms: 8 + x = -10.049875621 Solving 8 + x = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -10.049875621 + -8 Combine like terms: 8 + -8 = 0 0 + x = -10.049875621 + -8 x = -10.049875621 + -8 Combine like terms: -10.049875621 + -8 = -18.049875621 x = -18.049875621 Simplifying x = -18.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.049875621, -18.049875621}
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