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Simplifying -1X2 + 57X + -315 = 0 Reorder the terms: -315 + 57X + -1X2 = 0 Solving -315 + 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'. 315 + -57X + X2 = 0 Move the constant term to the right: Add '-315' to each side of the equation. 315 + -57X + -315 + X2 = 0 + -315 Reorder the terms: 315 + -315 + -57X + X2 = 0 + -315 Combine like terms: 315 + -315 = 0 0 + -57X + X2 = 0 + -315 -57X + X2 = 0 + -315 Combine like terms: 0 + -315 = -315 -57X + X2 = -315 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 = -315 + 812.25 Reorder the terms: 812.25 + -57X + X2 = -315 + 812.25 Combine like terms: -315 + 812.25 = 497.25 812.25 + -57X + X2 = 497.25 Factor a perfect square on the left side: (X + -28.5)(X + -28.5) = 497.25 Calculate the square root of the right side: 22.299103121 Break this problem into two subproblems by setting (X + -28.5) equal to 22.299103121 and -22.299103121.Subproblem 1
X + -28.5 = 22.299103121 Simplifying X + -28.5 = 22.299103121 Reorder the terms: -28.5 + X = 22.299103121 Solving -28.5 + X = 22.299103121 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 = 22.299103121 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + X = 22.299103121 + 28.5 X = 22.299103121 + 28.5 Combine like terms: 22.299103121 + 28.5 = 50.799103121 X = 50.799103121 Simplifying X = 50.799103121Subproblem 2
X + -28.5 = -22.299103121 Simplifying X + -28.5 = -22.299103121 Reorder the terms: -28.5 + X = -22.299103121 Solving -28.5 + X = -22.299103121 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 = -22.299103121 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + X = -22.299103121 + 28.5 X = -22.299103121 + 28.5 Combine like terms: -22.299103121 + 28.5 = 6.200896879 X = 6.200896879 Simplifying X = 6.200896879Solution
The solution to the problem is based on the solutions from the subproblems. X = {50.799103121, 6.200896879}
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