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Simplifying 2x2 + 19x = 172 Reorder the terms: 19x + 2x2 = 172 Solving 19x + 2x2 = 172 Solving for variable 'x'. Reorder the terms: -172 + 19x + 2x2 = 172 + -172 Combine like terms: 172 + -172 = 0 -172 + 19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -86 + 9.5x + x2 = 0 Move the constant term to the right: Add '86' to each side of the equation. -86 + 9.5x + 86 + x2 = 0 + 86 Reorder the terms: -86 + 86 + 9.5x + x2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + 9.5x + x2 = 0 + 86 9.5x + x2 = 0 + 86 Combine like terms: 0 + 86 = 86 9.5x + x2 = 86 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = 86 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = 86 + 22.5625 Combine like terms: 86 + 22.5625 = 108.5625 22.5625 + 9.5x + x2 = 108.5625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 108.5625 Calculate the square root of the right side: 10.419332992 Break this problem into two subproblems by setting (x + 4.75) equal to 10.419332992 and -10.419332992.Subproblem 1
x + 4.75 = 10.419332992 Simplifying x + 4.75 = 10.419332992 Reorder the terms: 4.75 + x = 10.419332992 Solving 4.75 + x = 10.419332992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 10.419332992 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 10.419332992 + -4.75 x = 10.419332992 + -4.75 Combine like terms: 10.419332992 + -4.75 = 5.669332992 x = 5.669332992 Simplifying x = 5.669332992Subproblem 2
x + 4.75 = -10.419332992 Simplifying x + 4.75 = -10.419332992 Reorder the terms: 4.75 + x = -10.419332992 Solving 4.75 + x = -10.419332992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -10.419332992 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -10.419332992 + -4.75 x = -10.419332992 + -4.75 Combine like terms: -10.419332992 + -4.75 = -15.169332992 x = -15.169332992 Simplifying x = -15.169332992Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.669332992, -15.169332992}
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