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Simplifying 5x2 + 764x + -2100 = 0 Reorder the terms: -2100 + 764x + 5x2 = 0 Solving -2100 + 764x + 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'. -420 + 152.8x + x2 = 0 Move the constant term to the right: Add '420' to each side of the equation. -420 + 152.8x + 420 + x2 = 0 + 420 Reorder the terms: -420 + 420 + 152.8x + x2 = 0 + 420 Combine like terms: -420 + 420 = 0 0 + 152.8x + x2 = 0 + 420 152.8x + x2 = 0 + 420 Combine like terms: 0 + 420 = 420 152.8x + x2 = 420 The x term is 152.8x. Take half its coefficient (76.4). Square it (5836.96) and add it to both sides. Add '5836.96' to each side of the equation. 152.8x + 5836.96 + x2 = 420 + 5836.96 Reorder the terms: 5836.96 + 152.8x + x2 = 420 + 5836.96 Combine like terms: 420 + 5836.96 = 6256.96 5836.96 + 152.8x + x2 = 6256.96 Factor a perfect square on the left side: (x + 76.4)(x + 76.4) = 6256.96 Calculate the square root of the right side: 79.100948161 Break this problem into two subproblems by setting (x + 76.4) equal to 79.100948161 and -79.100948161.Subproblem 1
x + 76.4 = 79.100948161 Simplifying x + 76.4 = 79.100948161 Reorder the terms: 76.4 + x = 79.100948161 Solving 76.4 + x = 79.100948161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-76.4' to each side of the equation. 76.4 + -76.4 + x = 79.100948161 + -76.4 Combine like terms: 76.4 + -76.4 = 0.0 0.0 + x = 79.100948161 + -76.4 x = 79.100948161 + -76.4 Combine like terms: 79.100948161 + -76.4 = 2.700948161 x = 2.700948161 Simplifying x = 2.700948161Subproblem 2
x + 76.4 = -79.100948161 Simplifying x + 76.4 = -79.100948161 Reorder the terms: 76.4 + x = -79.100948161 Solving 76.4 + x = -79.100948161 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-76.4' to each side of the equation. 76.4 + -76.4 + x = -79.100948161 + -76.4 Combine like terms: 76.4 + -76.4 = 0.0 0.0 + x = -79.100948161 + -76.4 x = -79.100948161 + -76.4 Combine like terms: -79.100948161 + -76.4 = -155.500948161 x = -155.500948161 Simplifying x = -155.500948161Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.700948161, -155.500948161}
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