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Simplifying 0.5x2 = 2x + -0.3 Reorder the terms: 0.5x2 = -0.3 + 2x Solving 0.5x2 = -0.3 + 2x Solving for variable 'x'. Reorder the terms: 0.3 + -2x + 0.5x2 = -0.3 + 2x + 0.3 + -2x Reorder the terms: 0.3 + -2x + 0.5x2 = -0.3 + 0.3 + 2x + -2x Combine like terms: -0.3 + 0.3 = 0.0 0.3 + -2x + 0.5x2 = 0.0 + 2x + -2x 0.3 + -2x + 0.5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 0.3 + -2x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 0.6 + -4x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -4x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -4x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -4x + x2 = 0 + -0.6 -4x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -4x + x2 = -0.6 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -0.6 + 4 Reorder the terms: 4 + -4x + x2 = -0.6 + 4 Combine like terms: -0.6 + 4 = 3.4 4 + -4x + x2 = 3.4 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.4 Calculate the square root of the right side: 1.843908891 Break this problem into two subproblems by setting (x + -2) equal to 1.843908891 and -1.843908891.Subproblem 1
x + -2 = 1.843908891 Simplifying x + -2 = 1.843908891 Reorder the terms: -2 + x = 1.843908891 Solving -2 + x = 1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.843908891 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.843908891 + 2 x = 1.843908891 + 2 Combine like terms: 1.843908891 + 2 = 3.843908891 x = 3.843908891 Simplifying x = 3.843908891Subproblem 2
x + -2 = -1.843908891 Simplifying x + -2 = -1.843908891 Reorder the terms: -2 + x = -1.843908891 Solving -2 + x = -1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.843908891 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.843908891 + 2 x = -1.843908891 + 2 Combine like terms: -1.843908891 + 2 = 0.156091109 x = 0.156091109 Simplifying x = 0.156091109Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.843908891, 0.156091109}
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