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Simplifying 5x2 + -98x + 260 = 0 Reorder the terms: 260 + -98x + 5x2 = 0 Solving 260 + -98x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 52 + -19.6x + x2 = 0 Move the constant term to the right: Add '-52' to each side of the equation. 52 + -19.6x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + -19.6x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -19.6x + x2 = 0 + -52 -19.6x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 -19.6x + x2 = -52 The x term is -19.6x. Take half its coefficient (-9.8). Square it (96.04) and add it to both sides. Add '96.04' to each side of the equation. -19.6x + 96.04 + x2 = -52 + 96.04 Reorder the terms: 96.04 + -19.6x + x2 = -52 + 96.04 Combine like terms: -52 + 96.04 = 44.04 96.04 + -19.6x + x2 = 44.04 Factor a perfect square on the left side: (x + -9.8)(x + -9.8) = 44.04 Calculate the square root of the right side: 6.636264009 Break this problem into two subproblems by setting (x + -9.8) equal to 6.636264009 and -6.636264009.Subproblem 1
x + -9.8 = 6.636264009 Simplifying x + -9.8 = 6.636264009 Reorder the terms: -9.8 + x = 6.636264009 Solving -9.8 + x = 6.636264009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.8' to each side of the equation. -9.8 + 9.8 + x = 6.636264009 + 9.8 Combine like terms: -9.8 + 9.8 = 0.0 0.0 + x = 6.636264009 + 9.8 x = 6.636264009 + 9.8 Combine like terms: 6.636264009 + 9.8 = 16.436264009 x = 16.436264009 Simplifying x = 16.436264009Subproblem 2
x + -9.8 = -6.636264009 Simplifying x + -9.8 = -6.636264009 Reorder the terms: -9.8 + x = -6.636264009 Solving -9.8 + x = -6.636264009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.8' to each side of the equation. -9.8 + 9.8 + x = -6.636264009 + 9.8 Combine like terms: -9.8 + 9.8 = 0.0 0.0 + x = -6.636264009 + 9.8 x = -6.636264009 + 9.8 Combine like terms: -6.636264009 + 9.8 = 3.163735991 x = 3.163735991 Simplifying x = 3.163735991Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.436264009, 3.163735991}
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