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Simplifying 0 = -0.5x2 + 3x + -2.8 Reorder the terms: 0 = -2.8 + 3x + -0.5x2 Solving 0 = -2.8 + 3x + -0.5x2 Solving for variable 'x'. Combine like terms: 0 + 2.8 = 2.8 2.8 + -3x + 0.5x2 = -2.8 + 3x + -0.5x2 + 2.8 + -3x + 0.5x2 Reorder the terms: 2.8 + -3x + 0.5x2 = -2.8 + 2.8 + 3x + -3x + -0.5x2 + 0.5x2 Combine like terms: -2.8 + 2.8 = 0.0 2.8 + -3x + 0.5x2 = 0.0 + 3x + -3x + -0.5x2 + 0.5x2 2.8 + -3x + 0.5x2 = 3x + -3x + -0.5x2 + 0.5x2 Combine like terms: 3x + -3x = 0 2.8 + -3x + 0.5x2 = 0 + -0.5x2 + 0.5x2 2.8 + -3x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 2.8 + -3x + 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'. 5.6 + -6x + x2 = 0 Move the constant term to the right: Add '-5.6' to each side of the equation. 5.6 + -6x + -5.6 + x2 = 0 + -5.6 Reorder the terms: 5.6 + -5.6 + -6x + x2 = 0 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + -6x + x2 = 0 + -5.6 -6x + x2 = 0 + -5.6 Combine like terms: 0 + -5.6 = -5.6 -6x + x2 = -5.6 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -5.6 + 9 Reorder the terms: 9 + -6x + x2 = -5.6 + 9 Combine like terms: -5.6 + 9 = 3.4 9 + -6x + x2 = 3.4 Factor a perfect square on the left side: (x + -3)(x + -3) = 3.4 Calculate the square root of the right side: 1.843908891 Break this problem into two subproblems by setting (x + -3) equal to 1.843908891 and -1.843908891.Subproblem 1
x + -3 = 1.843908891 Simplifying x + -3 = 1.843908891 Reorder the terms: -3 + x = 1.843908891 Solving -3 + x = 1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 1.843908891 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.843908891 + 3 x = 1.843908891 + 3 Combine like terms: 1.843908891 + 3 = 4.843908891 x = 4.843908891 Simplifying x = 4.843908891Subproblem 2
x + -3 = -1.843908891 Simplifying x + -3 = -1.843908891 Reorder the terms: -3 + x = -1.843908891 Solving -3 + x = -1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -1.843908891 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.843908891 + 3 x = -1.843908891 + 3 Combine like terms: -1.843908891 + 3 = 1.156091109 x = 1.156091109 Simplifying x = 1.156091109Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.843908891, 1.156091109}
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