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Simplifying 4x2 + -121x + 885 = 0 Reorder the terms: 885 + -121x + 4x2 = 0 Solving 885 + -121x + 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'. 221.25 + -30.25x + x2 = 0 Move the constant term to the right: Add '-221.25' to each side of the equation. 221.25 + -30.25x + -221.25 + x2 = 0 + -221.25 Reorder the terms: 221.25 + -221.25 + -30.25x + x2 = 0 + -221.25 Combine like terms: 221.25 + -221.25 = 0.00 0.00 + -30.25x + x2 = 0 + -221.25 -30.25x + x2 = 0 + -221.25 Combine like terms: 0 + -221.25 = -221.25 -30.25x + x2 = -221.25 The x term is -30.25x. Take half its coefficient (-15.125). Square it (228.765625) and add it to both sides. Add '228.765625' to each side of the equation. -30.25x + 228.765625 + x2 = -221.25 + 228.765625 Reorder the terms: 228.765625 + -30.25x + x2 = -221.25 + 228.765625 Combine like terms: -221.25 + 228.765625 = 7.515625 228.765625 + -30.25x + x2 = 7.515625 Factor a perfect square on the left side: (x + -15.125)(x + -15.125) = 7.515625 Calculate the square root of the right side: 2.741464025 Break this problem into two subproblems by setting (x + -15.125) equal to 2.741464025 and -2.741464025.Subproblem 1
x + -15.125 = 2.741464025 Simplifying x + -15.125 = 2.741464025 Reorder the terms: -15.125 + x = 2.741464025 Solving -15.125 + x = 2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.125' to each side of the equation. -15.125 + 15.125 + x = 2.741464025 + 15.125 Combine like terms: -15.125 + 15.125 = 0.000 0.000 + x = 2.741464025 + 15.125 x = 2.741464025 + 15.125 Combine like terms: 2.741464025 + 15.125 = 17.866464025 x = 17.866464025 Simplifying x = 17.866464025Subproblem 2
x + -15.125 = -2.741464025 Simplifying x + -15.125 = -2.741464025 Reorder the terms: -15.125 + x = -2.741464025 Solving -15.125 + x = -2.741464025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.125' to each side of the equation. -15.125 + 15.125 + x = -2.741464025 + 15.125 Combine like terms: -15.125 + 15.125 = 0.000 0.000 + x = -2.741464025 + 15.125 x = -2.741464025 + 15.125 Combine like terms: -2.741464025 + 15.125 = 12.383535975 x = 12.383535975 Simplifying x = 12.383535975Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.866464025, 12.383535975}
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