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Simplifying 2x2 + 120x + -1179 = 0 Reorder the terms: -1179 + 120x + 2x2 = 0 Solving -1179 + 120x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -589.5 + 60x + x2 = 0 Move the constant term to the right: Add '589.5' to each side of the equation. -589.5 + 60x + 589.5 + x2 = 0 + 589.5 Reorder the terms: -589.5 + 589.5 + 60x + x2 = 0 + 589.5 Combine like terms: -589.5 + 589.5 = 0.0 0.0 + 60x + x2 = 0 + 589.5 60x + x2 = 0 + 589.5 Combine like terms: 0 + 589.5 = 589.5 60x + x2 = 589.5 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = 589.5 + 900 Reorder the terms: 900 + 60x + x2 = 589.5 + 900 Combine like terms: 589.5 + 900 = 1489.5 900 + 60x + x2 = 1489.5 Factor a perfect square on the left side: (x + 30)(x + 30) = 1489.5 Calculate the square root of the right side: 38.594040991 Break this problem into two subproblems by setting (x + 30) equal to 38.594040991 and -38.594040991.Subproblem 1
x + 30 = 38.594040991 Simplifying x + 30 = 38.594040991 Reorder the terms: 30 + x = 38.594040991 Solving 30 + x = 38.594040991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 38.594040991 + -30 Combine like terms: 30 + -30 = 0 0 + x = 38.594040991 + -30 x = 38.594040991 + -30 Combine like terms: 38.594040991 + -30 = 8.594040991 x = 8.594040991 Simplifying x = 8.594040991Subproblem 2
x + 30 = -38.594040991 Simplifying x + 30 = -38.594040991 Reorder the terms: 30 + x = -38.594040991 Solving 30 + x = -38.594040991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -38.594040991 + -30 Combine like terms: 30 + -30 = 0 0 + x = -38.594040991 + -30 x = -38.594040991 + -30 Combine like terms: -38.594040991 + -30 = -68.594040991 x = -68.594040991 Simplifying x = -68.594040991Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.594040991, -68.594040991}
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