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Simplifying 53x2 + -85x + -130 = 0 Reorder the terms: -130 + -85x + 53x2 = 0 Solving -130 + -85x + 53x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 53 the coefficient of the squared term: Divide each side by '53'. -2.452830189 + -1.603773585x + x2 = 0 Move the constant term to the right: Add '2.452830189' to each side of the equation. -2.452830189 + -1.603773585x + 2.452830189 + x2 = 0 + 2.452830189 Reorder the terms: -2.452830189 + 2.452830189 + -1.603773585x + x2 = 0 + 2.452830189 Combine like terms: -2.452830189 + 2.452830189 = 0.000000000 0.000000000 + -1.603773585x + x2 = 0 + 2.452830189 -1.603773585x + x2 = 0 + 2.452830189 Combine like terms: 0 + 2.452830189 = 2.452830189 -1.603773585x + x2 = 2.452830189 The x term is -1.603773585x. Take half its coefficient (-0.8018867925). Square it (0.6430224280) and add it to both sides. Add '0.6430224280' to each side of the equation. -1.603773585x + 0.6430224280 + x2 = 2.452830189 + 0.6430224280 Reorder the terms: 0.6430224280 + -1.603773585x + x2 = 2.452830189 + 0.6430224280 Combine like terms: 2.452830189 + 0.6430224280 = 3.095852617 0.6430224280 + -1.603773585x + x2 = 3.095852617 Factor a perfect square on the left side: (x + -0.8018867925)(x + -0.8018867925) = 3.095852617 Calculate the square root of the right side: 1.759503514 Break this problem into two subproblems by setting (x + -0.8018867925) equal to 1.759503514 and -1.759503514.Subproblem 1
x + -0.8018867925 = 1.759503514 Simplifying x + -0.8018867925 = 1.759503514 Reorder the terms: -0.8018867925 + x = 1.759503514 Solving -0.8018867925 + x = 1.759503514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8018867925' to each side of the equation. -0.8018867925 + 0.8018867925 + x = 1.759503514 + 0.8018867925 Combine like terms: -0.8018867925 + 0.8018867925 = 0.0000000000 0.0000000000 + x = 1.759503514 + 0.8018867925 x = 1.759503514 + 0.8018867925 Combine like terms: 1.759503514 + 0.8018867925 = 2.5613903065 x = 2.5613903065 Simplifying x = 2.5613903065Subproblem 2
x + -0.8018867925 = -1.759503514 Simplifying x + -0.8018867925 = -1.759503514 Reorder the terms: -0.8018867925 + x = -1.759503514 Solving -0.8018867925 + x = -1.759503514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8018867925' to each side of the equation. -0.8018867925 + 0.8018867925 + x = -1.759503514 + 0.8018867925 Combine like terms: -0.8018867925 + 0.8018867925 = 0.0000000000 0.0000000000 + x = -1.759503514 + 0.8018867925 x = -1.759503514 + 0.8018867925 Combine like terms: -1.759503514 + 0.8018867925 = -0.9576167215 x = -0.9576167215 Simplifying x = -0.9576167215Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5613903065, -0.9576167215}
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