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Simplifying 5x2 + -152x + -983 = 0 Reorder the terms: -983 + -152x + 5x2 = 0 Solving -983 + -152x + 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'. -196.6 + -30.4x + x2 = 0 Move the constant term to the right: Add '196.6' to each side of the equation. -196.6 + -30.4x + 196.6 + x2 = 0 + 196.6 Reorder the terms: -196.6 + 196.6 + -30.4x + x2 = 0 + 196.6 Combine like terms: -196.6 + 196.6 = 0.0 0.0 + -30.4x + x2 = 0 + 196.6 -30.4x + x2 = 0 + 196.6 Combine like terms: 0 + 196.6 = 196.6 -30.4x + x2 = 196.6 The x term is -30.4x. Take half its coefficient (-15.2). Square it (231.04) and add it to both sides. Add '231.04' to each side of the equation. -30.4x + 231.04 + x2 = 196.6 + 231.04 Reorder the terms: 231.04 + -30.4x + x2 = 196.6 + 231.04 Combine like terms: 196.6 + 231.04 = 427.64 231.04 + -30.4x + x2 = 427.64 Factor a perfect square on the left side: (x + -15.2)(x + -15.2) = 427.64 Calculate the square root of the right side: 20.679458407 Break this problem into two subproblems by setting (x + -15.2) equal to 20.679458407 and -20.679458407.Subproblem 1
x + -15.2 = 20.679458407 Simplifying x + -15.2 = 20.679458407 Reorder the terms: -15.2 + x = 20.679458407 Solving -15.2 + x = 20.679458407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.2' to each side of the equation. -15.2 + 15.2 + x = 20.679458407 + 15.2 Combine like terms: -15.2 + 15.2 = 0.0 0.0 + x = 20.679458407 + 15.2 x = 20.679458407 + 15.2 Combine like terms: 20.679458407 + 15.2 = 35.879458407 x = 35.879458407 Simplifying x = 35.879458407Subproblem 2
x + -15.2 = -20.679458407 Simplifying x + -15.2 = -20.679458407 Reorder the terms: -15.2 + x = -20.679458407 Solving -15.2 + x = -20.679458407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.2' to each side of the equation. -15.2 + 15.2 + x = -20.679458407 + 15.2 Combine like terms: -15.2 + 15.2 = 0.0 0.0 + x = -20.679458407 + 15.2 x = -20.679458407 + 15.2 Combine like terms: -20.679458407 + 15.2 = -5.479458407 x = -5.479458407 Simplifying x = -5.479458407Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.879458407, -5.479458407}
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