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Simplifying -1x2 + 2x = -54 Reorder the terms: 2x + -1x2 = -54 Solving 2x + -1x2 = -54 Solving for variable 'x'. Reorder the terms: 54 + 2x + -1x2 = -54 + 54 Combine like terms: -54 + 54 = 0 54 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -54 + -2x + x2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + -2x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -2x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -2x + x2 = 0 + 54 -2x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -2x + x2 = 54 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 54 + 1 Reorder the terms: 1 + -2x + x2 = 54 + 1 Combine like terms: 54 + 1 = 55 1 + -2x + x2 = 55 Factor a perfect square on the left side: (x + -1)(x + -1) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + -1) equal to 7.416198487 and -7.416198487.Subproblem 1
x + -1 = 7.416198487 Simplifying x + -1 = 7.416198487 Reorder the terms: -1 + x = 7.416198487 Solving -1 + x = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 7.416198487 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.416198487 + 1 x = 7.416198487 + 1 Combine like terms: 7.416198487 + 1 = 8.416198487 x = 8.416198487 Simplifying x = 8.416198487Subproblem 2
x + -1 = -7.416198487 Simplifying x + -1 = -7.416198487 Reorder the terms: -1 + x = -7.416198487 Solving -1 + x = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -7.416198487 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.416198487 + 1 x = -7.416198487 + 1 Combine like terms: -7.416198487 + 1 = -6.416198487 x = -6.416198487 Simplifying x = -6.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.416198487, -6.416198487}
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