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Simplifying 54 + 16x + -1x2 = 0 Solving 54 + 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'. -54 + -16x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + -16x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -16x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -16x + x2 = 0 + 54 -16x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -16x + x2 = 54 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 = 54 + 64 Reorder the terms: 64 + -16x + x2 = 54 + 64 Combine like terms: 54 + 64 = 118 64 + -16x + x2 = 118 Factor a perfect square on the left side: (x + -8)(x + -8) = 118 Calculate the square root of the right side: 10.862780491 Break this problem into two subproblems by setting (x + -8) equal to 10.862780491 and -10.862780491.Subproblem 1
x + -8 = 10.862780491 Simplifying x + -8 = 10.862780491 Reorder the terms: -8 + x = 10.862780491 Solving -8 + x = 10.862780491 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 = 10.862780491 + 8 Combine like terms: -8 + 8 = 0 0 + x = 10.862780491 + 8 x = 10.862780491 + 8 Combine like terms: 10.862780491 + 8 = 18.862780491 x = 18.862780491 Simplifying x = 18.862780491Subproblem 2
x + -8 = -10.862780491 Simplifying x + -8 = -10.862780491 Reorder the terms: -8 + x = -10.862780491 Solving -8 + x = -10.862780491 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 = -10.862780491 + 8 Combine like terms: -8 + 8 = 0 0 + x = -10.862780491 + 8 x = -10.862780491 + 8 Combine like terms: -10.862780491 + 8 = -2.862780491 x = -2.862780491 Simplifying x = -2.862780491Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.862780491, -2.862780491}
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