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Simplifying 0 = x2 + 16x + 37 Reorder the terms: 0 = 37 + 16x + x2 Solving 0 = 37 + 16x + x2 Solving for variable 'x'. Combine like terms: 0 + -37 = -37 -37 + -16x + -1x2 = 37 + 16x + x2 + -37 + -16x + -1x2 Reorder the terms: -37 + -16x + -1x2 = 37 + -37 + 16x + -16x + x2 + -1x2 Combine like terms: 37 + -37 = 0 -37 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2 -37 + -16x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 -37 + -16x + -1x2 = 0 + x2 + -1x2 -37 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -37 + -16x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(37 + 16x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(37 + 16x + x2)' equal to zero and attempt to solve: Simplifying 37 + 16x + x2 = 0 Solving 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 = 27 64 + 16x + x2 = 27 Factor a perfect square on the left side: (x + 8)(x + 8) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + 8) equal to 5.196152423 and -5.196152423.Subproblem 1
x + 8 = 5.196152423 Simplifying x + 8 = 5.196152423 Reorder the terms: 8 + x = 5.196152423 Solving 8 + x = 5.196152423 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 = 5.196152423 + -8 Combine like terms: 8 + -8 = 0 0 + x = 5.196152423 + -8 x = 5.196152423 + -8 Combine like terms: 5.196152423 + -8 = -2.803847577 x = -2.803847577 Simplifying x = -2.803847577Subproblem 2
x + 8 = -5.196152423 Simplifying x + 8 = -5.196152423 Reorder the terms: 8 + x = -5.196152423 Solving 8 + x = -5.196152423 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 = -5.196152423 + -8 Combine like terms: 8 + -8 = 0 0 + x = -5.196152423 + -8 x = -5.196152423 + -8 Combine like terms: -5.196152423 + -8 = -13.196152423 x = -13.196152423 Simplifying x = -13.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.803847577, -13.196152423}Solution
x = {-2.803847577, -13.196152423}
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