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Simplifying -1x2 + 48x + 322 = 0 Reorder the terms: 322 + 48x + -1x2 = 0 Solving 322 + 48x + -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'. -322 + -48x + x2 = 0 Move the constant term to the right: Add '322' to each side of the equation. -322 + -48x + 322 + x2 = 0 + 322 Reorder the terms: -322 + 322 + -48x + x2 = 0 + 322 Combine like terms: -322 + 322 = 0 0 + -48x + x2 = 0 + 322 -48x + x2 = 0 + 322 Combine like terms: 0 + 322 = 322 -48x + x2 = 322 The x term is -48x. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x + 576 + x2 = 322 + 576 Reorder the terms: 576 + -48x + x2 = 322 + 576 Combine like terms: 322 + 576 = 898 576 + -48x + x2 = 898 Factor a perfect square on the left side: (x + -24)(x + -24) = 898 Calculate the square root of the right side: 29.966648128 Break this problem into two subproblems by setting (x + -24) equal to 29.966648128 and -29.966648128.Subproblem 1
x + -24 = 29.966648128 Simplifying x + -24 = 29.966648128 Reorder the terms: -24 + x = 29.966648128 Solving -24 + x = 29.966648128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 29.966648128 + 24 Combine like terms: -24 + 24 = 0 0 + x = 29.966648128 + 24 x = 29.966648128 + 24 Combine like terms: 29.966648128 + 24 = 53.966648128 x = 53.966648128 Simplifying x = 53.966648128Subproblem 2
x + -24 = -29.966648128 Simplifying x + -24 = -29.966648128 Reorder the terms: -24 + x = -29.966648128 Solving -24 + x = -29.966648128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -29.966648128 + 24 Combine like terms: -24 + 24 = 0 0 + x = -29.966648128 + 24 x = -29.966648128 + 24 Combine like terms: -29.966648128 + 24 = -5.966648128 x = -5.966648128 Simplifying x = -5.966648128Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.966648128, -5.966648128}
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