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Simplifying x2 + 16x + 45 = 0 Reorder the terms: 45 + 16x + x2 = 0 Solving 45 + 16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + 16x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + 16x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 16x + x2 = 0 + -45 16x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 16x + x2 = -45 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 = -45 + 64 Reorder the terms: 64 + 16x + x2 = -45 + 64 Combine like terms: -45 + 64 = 19 64 + 16x + x2 = 19 Factor a perfect square on the left side: (x + 8)(x + 8) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 8) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 8 = 4.358898944 Simplifying x + 8 = 4.358898944 Reorder the terms: 8 + x = 4.358898944 Solving 8 + x = 4.358898944 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 = 4.358898944 + -8 Combine like terms: 8 + -8 = 0 0 + x = 4.358898944 + -8 x = 4.358898944 + -8 Combine like terms: 4.358898944 + -8 = -3.641101056 x = -3.641101056 Simplifying x = -3.641101056Subproblem 2
x + 8 = -4.358898944 Simplifying x + 8 = -4.358898944 Reorder the terms: 8 + x = -4.358898944 Solving 8 + x = -4.358898944 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 = -4.358898944 + -8 Combine like terms: 8 + -8 = 0 0 + x = -4.358898944 + -8 x = -4.358898944 + -8 Combine like terms: -4.358898944 + -8 = -12.358898944 x = -12.358898944 Simplifying x = -12.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.641101056, -12.358898944}
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