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Simplifying -1x2 + -16x + 52 = 0 Reorder the terms: 52 + -16x + -1x2 = 0 Solving 52 + -16x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -52 + 16x + x2 = 0 Move the constant term to the right: Add '52' to each side of the equation. -52 + 16x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 16x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 16x + x2 = 0 + 52 16x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 16x + x2 = 52 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 = 52 + 64 Reorder the terms: 64 + 16x + x2 = 52 + 64 Combine like terms: 52 + 64 = 116 64 + 16x + x2 = 116 Factor a perfect square on the left side: (x + 8)(x + 8) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (x + 8) equal to 10.770329614 and -10.770329614.Subproblem 1
x + 8 = 10.770329614 Simplifying x + 8 = 10.770329614 Reorder the terms: 8 + x = 10.770329614 Solving 8 + x = 10.770329614 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 = 10.770329614 + -8 Combine like terms: 8 + -8 = 0 0 + x = 10.770329614 + -8 x = 10.770329614 + -8 Combine like terms: 10.770329614 + -8 = 2.770329614 x = 2.770329614 Simplifying x = 2.770329614Subproblem 2
x + 8 = -10.770329614 Simplifying x + 8 = -10.770329614 Reorder the terms: 8 + x = -10.770329614 Solving 8 + x = -10.770329614 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 = -10.770329614 + -8 Combine like terms: 8 + -8 = 0 0 + x = -10.770329614 + -8 x = -10.770329614 + -8 Combine like terms: -10.770329614 + -8 = -18.770329614 x = -18.770329614 Simplifying x = -18.770329614Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.770329614, -18.770329614}
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