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Simplifying 2x2 + 60x = 319 Reorder the terms: 60x + 2x2 = 319 Solving 60x + 2x2 = 319 Solving for variable 'x'. Reorder the terms: -319 + 60x + 2x2 = 319 + -319 Combine like terms: 319 + -319 = 0 -319 + 60x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -159.5 + 30x + x2 = 0 Move the constant term to the right: Add '159.5' to each side of the equation. -159.5 + 30x + 159.5 + x2 = 0 + 159.5 Reorder the terms: -159.5 + 159.5 + 30x + x2 = 0 + 159.5 Combine like terms: -159.5 + 159.5 = 0.0 0.0 + 30x + x2 = 0 + 159.5 30x + x2 = 0 + 159.5 Combine like terms: 0 + 159.5 = 159.5 30x + x2 = 159.5 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 159.5 + 225 Reorder the terms: 225 + 30x + x2 = 159.5 + 225 Combine like terms: 159.5 + 225 = 384.5 225 + 30x + x2 = 384.5 Factor a perfect square on the left side: (x + 15)(x + 15) = 384.5 Calculate the square root of the right side: 19.608671551 Break this problem into two subproblems by setting (x + 15) equal to 19.608671551 and -19.608671551.Subproblem 1
x + 15 = 19.608671551 Simplifying x + 15 = 19.608671551 Reorder the terms: 15 + x = 19.608671551 Solving 15 + x = 19.608671551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 19.608671551 + -15 Combine like terms: 15 + -15 = 0 0 + x = 19.608671551 + -15 x = 19.608671551 + -15 Combine like terms: 19.608671551 + -15 = 4.608671551 x = 4.608671551 Simplifying x = 4.608671551Subproblem 2
x + 15 = -19.608671551 Simplifying x + 15 = -19.608671551 Reorder the terms: 15 + x = -19.608671551 Solving 15 + x = -19.608671551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -19.608671551 + -15 Combine like terms: 15 + -15 = 0 0 + x = -19.608671551 + -15 x = -19.608671551 + -15 Combine like terms: -19.608671551 + -15 = -34.608671551 x = -34.608671551 Simplifying x = -34.608671551Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.608671551, -34.608671551}
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