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Simplifying 63X + -1X2 = 50 Solving 63X + -1X2 = 50 Solving for variable 'X'. Reorder the terms: -50 + 63X + -1X2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 63X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 50 + -63X + X2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -63X + -50 + X2 = 0 + -50 Reorder the terms: 50 + -50 + -63X + X2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -63X + X2 = 0 + -50 -63X + X2 = 0 + -50 Combine like terms: 0 + -50 = -50 -63X + X2 = -50 The X term is -63X. Take half its coefficient (-31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. -63X + 992.25 + X2 = -50 + 992.25 Reorder the terms: 992.25 + -63X + X2 = -50 + 992.25 Combine like terms: -50 + 992.25 = 942.25 992.25 + -63X + X2 = 942.25 Factor a perfect square on the left side: (X + -31.5)(X + -31.5) = 942.25 Calculate the square root of the right side: 30.696090956 Break this problem into two subproblems by setting (X + -31.5) equal to 30.696090956 and -30.696090956.Subproblem 1
X + -31.5 = 30.696090956 Simplifying X + -31.5 = 30.696090956 Reorder the terms: -31.5 + X = 30.696090956 Solving -31.5 + X = 30.696090956 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '31.5' to each side of the equation. -31.5 + 31.5 + X = 30.696090956 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + X = 30.696090956 + 31.5 X = 30.696090956 + 31.5 Combine like terms: 30.696090956 + 31.5 = 62.196090956 X = 62.196090956 Simplifying X = 62.196090956Subproblem 2
X + -31.5 = -30.696090956 Simplifying X + -31.5 = -30.696090956 Reorder the terms: -31.5 + X = -30.696090956 Solving -31.5 + X = -30.696090956 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '31.5' to each side of the equation. -31.5 + 31.5 + X = -30.696090956 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + X = -30.696090956 + 31.5 X = -30.696090956 + 31.5 Combine like terms: -30.696090956 + 31.5 = 0.803909044 X = 0.803909044 Simplifying X = 0.803909044Solution
The solution to the problem is based on the solutions from the subproblems. X = {62.196090956, 0.803909044}
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