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Simplifying x2 + 8x + -73 = 0 Reorder the terms: -73 + 8x + x2 = 0 Solving -73 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + 8x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + 8x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + 8x + x2 = 0 + 73 8x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 8x + x2 = 73 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 = 73 + 16 Reorder the terms: 16 + 8x + x2 = 73 + 16 Combine like terms: 73 + 16 = 89 16 + 8x + x2 = 89 Factor a perfect square on the left side: (x + 4)(x + 4) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + 4) equal to 9.433981132 and -9.433981132.Subproblem 1
x + 4 = 9.433981132 Simplifying x + 4 = 9.433981132 Reorder the terms: 4 + x = 9.433981132 Solving 4 + x = 9.433981132 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 = 9.433981132 + -4 Combine like terms: 4 + -4 = 0 0 + x = 9.433981132 + -4 x = 9.433981132 + -4 Combine like terms: 9.433981132 + -4 = 5.433981132 x = 5.433981132 Simplifying x = 5.433981132Subproblem 2
x + 4 = -9.433981132 Simplifying x + 4 = -9.433981132 Reorder the terms: 4 + x = -9.433981132 Solving 4 + x = -9.433981132 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 = -9.433981132 + -4 Combine like terms: 4 + -4 = 0 0 + x = -9.433981132 + -4 x = -9.433981132 + -4 Combine like terms: -9.433981132 + -4 = -13.433981132 x = -13.433981132 Simplifying x = -13.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.433981132, -13.433981132}
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