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Simplifying 0.25x2 + 15x + -1840 = 0 Reorder the terms: -1840 + 15x + 0.25x2 = 0 Solving -1840 + 15x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -7360 + 60x + x2 = 0 Move the constant term to the right: Add '7360' to each side of the equation. -7360 + 60x + 7360 + x2 = 0 + 7360 Reorder the terms: -7360 + 7360 + 60x + x2 = 0 + 7360 Combine like terms: -7360 + 7360 = 0 0 + 60x + x2 = 0 + 7360 60x + x2 = 0 + 7360 Combine like terms: 0 + 7360 = 7360 60x + x2 = 7360 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 = 7360 + 900 Reorder the terms: 900 + 60x + x2 = 7360 + 900 Combine like terms: 7360 + 900 = 8260 900 + 60x + x2 = 8260 Factor a perfect square on the left side: (x + 30)(x + 30) = 8260 Calculate the square root of the right side: 90.88454214 Break this problem into two subproblems by setting (x + 30) equal to 90.88454214 and -90.88454214.Subproblem 1
x + 30 = 90.88454214 Simplifying x + 30 = 90.88454214 Reorder the terms: 30 + x = 90.88454214 Solving 30 + x = 90.88454214 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 = 90.88454214 + -30 Combine like terms: 30 + -30 = 0 0 + x = 90.88454214 + -30 x = 90.88454214 + -30 Combine like terms: 90.88454214 + -30 = 60.88454214 x = 60.88454214 Simplifying x = 60.88454214Subproblem 2
x + 30 = -90.88454214 Simplifying x + 30 = -90.88454214 Reorder the terms: 30 + x = -90.88454214 Solving 30 + x = -90.88454214 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 = -90.88454214 + -30 Combine like terms: 30 + -30 = 0 0 + x = -90.88454214 + -30 x = -90.88454214 + -30 Combine like terms: -90.88454214 + -30 = -120.88454214 x = -120.88454214 Simplifying x = -120.88454214Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.88454214, -120.88454214}
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