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Simplifying x2 + 8x + -100 = 0 Reorder the terms: -100 + 8x + x2 = 0 Solving -100 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 8x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 8x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 8x + x2 = 0 + 100 8x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 8x + x2 = 100 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 = 100 + 16 Reorder the terms: 16 + 8x + x2 = 100 + 16 Combine like terms: 100 + 16 = 116 16 + 8x + x2 = 116 Factor a perfect square on the left side: (x + 4)(x + 4) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (x + 4) equal to 10.770329614 and -10.770329614.Subproblem 1
x + 4 = 10.770329614 Simplifying x + 4 = 10.770329614 Reorder the terms: 4 + x = 10.770329614 Solving 4 + x = 10.770329614 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 = 10.770329614 + -4 Combine like terms: 4 + -4 = 0 0 + x = 10.770329614 + -4 x = 10.770329614 + -4 Combine like terms: 10.770329614 + -4 = 6.770329614 x = 6.770329614 Simplifying x = 6.770329614Subproblem 2
x + 4 = -10.770329614 Simplifying x + 4 = -10.770329614 Reorder the terms: 4 + x = -10.770329614 Solving 4 + x = -10.770329614 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 = -10.770329614 + -4 Combine like terms: 4 + -4 = 0 0 + x = -10.770329614 + -4 x = -10.770329614 + -4 Combine like terms: -10.770329614 + -4 = -14.770329614 x = -14.770329614 Simplifying x = -14.770329614Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.770329614, -14.770329614}
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