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Simplifying 0.5x2 + -5x + 3.5 = (2.8) Reorder the terms: 3.5 + -5x + 0.5x2 = (2.8) 3.5 + -5x + 0.5x2 = 2.8 Solving 3.5 + -5x + 0.5x2 = 2.8 Solving for variable 'x'. Reorder the terms: 3.5 + -2.8 + -5x + 0.5x2 = 2.8 + -2.8 Combine like terms: 3.5 + -2.8 = 0.7 0.7 + -5x + 0.5x2 = 2.8 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.7 + -5x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 1.4 + -10x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -10x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -10x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -10x + x2 = 0 + -1.4 -10x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -10x + x2 = -1.4 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -1.4 + 25 Reorder the terms: 25 + -10x + x2 = -1.4 + 25 Combine like terms: -1.4 + 25 = 23.6 25 + -10x + x2 = 23.6 Factor a perfect square on the left side: (x + -5)(x + -5) = 23.6 Calculate the square root of the right side: 4.857983121 Break this problem into two subproblems by setting (x + -5) equal to 4.857983121 and -4.857983121.Subproblem 1
x + -5 = 4.857983121 Simplifying x + -5 = 4.857983121 Reorder the terms: -5 + x = 4.857983121 Solving -5 + x = 4.857983121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.857983121 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.857983121 + 5 x = 4.857983121 + 5 Combine like terms: 4.857983121 + 5 = 9.857983121 x = 9.857983121 Simplifying x = 9.857983121Subproblem 2
x + -5 = -4.857983121 Simplifying x + -5 = -4.857983121 Reorder the terms: -5 + x = -4.857983121 Solving -5 + x = -4.857983121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.857983121 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.857983121 + 5 x = -4.857983121 + 5 Combine like terms: -4.857983121 + 5 = 0.142016879 x = 0.142016879 Simplifying x = 0.142016879Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.857983121, 0.142016879}
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