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Simplifying 49x + -1x2 = -30 Solving 49x + -1x2 = -30 Solving for variable 'x'. Reorder the terms: 30 + 49x + -1x2 = -30 + 30 Combine like terms: -30 + 30 = 0 30 + 49x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + -49x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -49x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -49x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -49x + x2 = 0 + 30 -49x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -49x + x2 = 30 The x term is -49x. Take half its coefficient (-24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. -49x + 600.25 + x2 = 30 + 600.25 Reorder the terms: 600.25 + -49x + x2 = 30 + 600.25 Combine like terms: 30 + 600.25 = 630.25 600.25 + -49x + x2 = 630.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 630.25 Calculate the square root of the right side: 25.104780421 Break this problem into two subproblems by setting (x + -24.5) equal to 25.104780421 and -25.104780421.Subproblem 1
x + -24.5 = 25.104780421 Simplifying x + -24.5 = 25.104780421 Reorder the terms: -24.5 + x = 25.104780421 Solving -24.5 + x = 25.104780421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = 25.104780421 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 25.104780421 + 24.5 x = 25.104780421 + 24.5 Combine like terms: 25.104780421 + 24.5 = 49.604780421 x = 49.604780421 Simplifying x = 49.604780421Subproblem 2
x + -24.5 = -25.104780421 Simplifying x + -24.5 = -25.104780421 Reorder the terms: -24.5 + x = -25.104780421 Solving -24.5 + x = -25.104780421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = -25.104780421 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -25.104780421 + 24.5 x = -25.104780421 + 24.5 Combine like terms: -25.104780421 + 24.5 = -0.604780421 x = -0.604780421 Simplifying x = -0.604780421Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.604780421, -0.604780421}
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