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Simplifying 4x2 + -112x + 381 = 0 Reorder the terms: 381 + -112x + 4x2 = 0 Solving 381 + -112x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 95.25 + -28x + x2 = 0 Move the constant term to the right: Add '-95.25' to each side of the equation. 95.25 + -28x + -95.25 + x2 = 0 + -95.25 Reorder the terms: 95.25 + -95.25 + -28x + x2 = 0 + -95.25 Combine like terms: 95.25 + -95.25 = 0.00 0.00 + -28x + x2 = 0 + -95.25 -28x + x2 = 0 + -95.25 Combine like terms: 0 + -95.25 = -95.25 -28x + x2 = -95.25 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -95.25 + 196 Reorder the terms: 196 + -28x + x2 = -95.25 + 196 Combine like terms: -95.25 + 196 = 100.75 196 + -28x + x2 = 100.75 Factor a perfect square on the left side: (x + -14)(x + -14) = 100.75 Calculate the square root of the right side: 10.03742995 Break this problem into two subproblems by setting (x + -14) equal to 10.03742995 and -10.03742995.Subproblem 1
x + -14 = 10.03742995 Simplifying x + -14 = 10.03742995 Reorder the terms: -14 + x = 10.03742995 Solving -14 + x = 10.03742995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 10.03742995 + 14 Combine like terms: -14 + 14 = 0 0 + x = 10.03742995 + 14 x = 10.03742995 + 14 Combine like terms: 10.03742995 + 14 = 24.03742995 x = 24.03742995 Simplifying x = 24.03742995Subproblem 2
x + -14 = -10.03742995 Simplifying x + -14 = -10.03742995 Reorder the terms: -14 + x = -10.03742995 Solving -14 + x = -10.03742995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -10.03742995 + 14 Combine like terms: -14 + 14 = 0 0 + x = -10.03742995 + 14 x = -10.03742995 + 14 Combine like terms: -10.03742995 + 14 = 3.96257005 x = 3.96257005 Simplifying x = 3.96257005Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.03742995, 3.96257005}
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