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Simplifying x2 + 8x = 37 Reorder the terms: 8x + x2 = 37 Solving 8x + x2 = 37 Solving for variable 'x'. Reorder the terms: -37 + 8x + x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 8x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + 8x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 8x + x2 = 0 + 37 8x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 8x + x2 = 37 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 37 + 16 Reorder the terms: 16 + 8x + x2 = 37 + 16 Combine like terms: 37 + 16 = 53 16 + 8x + x2 = 53 Factor a perfect square on the left side: (x + 4)(x + 4) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + 4) equal to 7.280109889 and -7.280109889.Subproblem 1
x + 4 = 7.280109889 Simplifying x + 4 = 7.280109889 Reorder the terms: 4 + x = 7.280109889 Solving 4 + x = 7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 7.280109889 + -4 Combine like terms: 4 + -4 = 0 0 + x = 7.280109889 + -4 x = 7.280109889 + -4 Combine like terms: 7.280109889 + -4 = 3.280109889 x = 3.280109889 Simplifying x = 3.280109889Subproblem 2
x + 4 = -7.280109889 Simplifying x + 4 = -7.280109889 Reorder the terms: 4 + x = -7.280109889 Solving 4 + x = -7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -7.280109889 + -4 Combine like terms: 4 + -4 = 0 0 + x = -7.280109889 + -4 x = -7.280109889 + -4 Combine like terms: -7.280109889 + -4 = -11.280109889 x = -11.280109889 Simplifying x = -11.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.280109889, -11.280109889}
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