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Simplifying x2 + -16x + 37 = 0 Reorder the terms: 37 + -16x + x2 = 0 Solving 37 + -16x + x2 = 0 Solving for variable 'x'. 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 = 13.196152423 x = 13.196152423 Simplifying x = 13.196152423Subproblem 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 = 2.803847577 x = 2.803847577 Simplifying x = 2.803847577Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.196152423, 2.803847577}
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