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Simplifying 0 = -0.3x2 + 3x + 4 Reorder the terms: 0 = 4 + 3x + -0.3x2 Solving 0 = 4 + 3x + -0.3x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -3x + 0.3x2 = 4 + 3x + -0.3x2 + -4 + -3x + 0.3x2 Reorder the terms: -4 + -3x + 0.3x2 = 4 + -4 + 3x + -3x + -0.3x2 + 0.3x2 Combine like terms: 4 + -4 = 0 -4 + -3x + 0.3x2 = 0 + 3x + -3x + -0.3x2 + 0.3x2 -4 + -3x + 0.3x2 = 3x + -3x + -0.3x2 + 0.3x2 Combine like terms: 3x + -3x = 0 -4 + -3x + 0.3x2 = 0 + -0.3x2 + 0.3x2 -4 + -3x + 0.3x2 = -0.3x2 + 0.3x2 Combine like terms: -0.3x2 + 0.3x2 = 0.0 -4 + -3x + 0.3x2 = 0.0 Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. -13.33333333 + -10x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -10x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -10x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -10x + x2 = 0 + 13.33333333 -10x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -10x + x2 = 13.33333333 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 = 13.33333333 + 25 Reorder the terms: 25 + -10x + x2 = 13.33333333 + 25 Combine like terms: 13.33333333 + 25 = 38.33333333 25 + -10x + x2 = 38.33333333 Factor a perfect square on the left side: (x + -5)(x + -5) = 38.33333333 Calculate the square root of the right side: 6.191391873 Break this problem into two subproblems by setting (x + -5) equal to 6.191391873 and -6.191391873.Subproblem 1
x + -5 = 6.191391873 Simplifying x + -5 = 6.191391873 Reorder the terms: -5 + x = 6.191391873 Solving -5 + x = 6.191391873 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 = 6.191391873 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.191391873 + 5 x = 6.191391873 + 5 Combine like terms: 6.191391873 + 5 = 11.191391873 x = 11.191391873 Simplifying x = 11.191391873Subproblem 2
x + -5 = -6.191391873 Simplifying x + -5 = -6.191391873 Reorder the terms: -5 + x = -6.191391873 Solving -5 + x = -6.191391873 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 = -6.191391873 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.191391873 + 5 x = -6.191391873 + 5 Combine like terms: -6.191391873 + 5 = -1.191391873 x = -1.191391873 Simplifying x = -1.191391873Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.191391873, -1.191391873}
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