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Simplifying 240 + 57x + -1x2 = 0 Solving 240 + 57x + -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'. -240 + -57x + x2 = 0 Move the constant term to the right: Add '240' to each side of the equation. -240 + -57x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + -57x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + -57x + x2 = 0 + 240 -57x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 -57x + x2 = 240 The x term is -57x. Take half its coefficient (-28.5). Square it (812.25) and add it to both sides. Add '812.25' to each side of the equation. -57x + 812.25 + x2 = 240 + 812.25 Reorder the terms: 812.25 + -57x + x2 = 240 + 812.25 Combine like terms: 240 + 812.25 = 1052.25 812.25 + -57x + x2 = 1052.25 Factor a perfect square on the left side: (x + -28.5)(x + -28.5) = 1052.25 Calculate the square root of the right side: 32.438403167 Break this problem into two subproblems by setting (x + -28.5) equal to 32.438403167 and -32.438403167.Subproblem 1
x + -28.5 = 32.438403167 Simplifying x + -28.5 = 32.438403167 Reorder the terms: -28.5 + x = 32.438403167 Solving -28.5 + x = 32.438403167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.5' to each side of the equation. -28.5 + 28.5 + x = 32.438403167 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + x = 32.438403167 + 28.5 x = 32.438403167 + 28.5 Combine like terms: 32.438403167 + 28.5 = 60.938403167 x = 60.938403167 Simplifying x = 60.938403167Subproblem 2
x + -28.5 = -32.438403167 Simplifying x + -28.5 = -32.438403167 Reorder the terms: -28.5 + x = -32.438403167 Solving -28.5 + x = -32.438403167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.5' to each side of the equation. -28.5 + 28.5 + x = -32.438403167 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + x = -32.438403167 + 28.5 x = -32.438403167 + 28.5 Combine like terms: -32.438403167 + 28.5 = -3.938403167 x = -3.938403167 Simplifying x = -3.938403167Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.938403167, -3.938403167}
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