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Simplifying 0 = 0.6x2 + -3x + -1.5 Reorder the terms: 0 = -1.5 + -3x + 0.6x2 Solving 0 = -1.5 + -3x + 0.6x2 Solving for variable 'x'. Combine like terms: 0 + 1.5 = 1.5 1.5 + 3x + -0.6x2 = -1.5 + -3x + 0.6x2 + 1.5 + 3x + -0.6x2 Reorder the terms: 1.5 + 3x + -0.6x2 = -1.5 + 1.5 + -3x + 3x + 0.6x2 + -0.6x2 Combine like terms: -1.5 + 1.5 = 0.0 1.5 + 3x + -0.6x2 = 0.0 + -3x + 3x + 0.6x2 + -0.6x2 1.5 + 3x + -0.6x2 = -3x + 3x + 0.6x2 + -0.6x2 Combine like terms: -3x + 3x = 0 1.5 + 3x + -0.6x2 = 0 + 0.6x2 + -0.6x2 1.5 + 3x + -0.6x2 = 0.6x2 + -0.6x2 Combine like terms: 0.6x2 + -0.6x2 = 0.0 1.5 + 3x + -0.6x2 = 0.0 Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. -2.5 + -5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -5x + x2 = 0 + 2.5 -5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -5x + x2 = 2.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 2.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 2.5 + 6.25 Combine like terms: 2.5 + 6.25 = 8.75 6.25 + -5x + x2 = 8.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (x + -2.5) equal to 2.958039892 and -2.958039892.Subproblem 1
x + -2.5 = 2.958039892 Simplifying x + -2.5 = 2.958039892 Reorder the terms: -2.5 + x = 2.958039892 Solving -2.5 + x = 2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.958039892 + 2.5 x = 2.958039892 + 2.5 Combine like terms: 2.958039892 + 2.5 = 5.458039892 x = 5.458039892 Simplifying x = 5.458039892Subproblem 2
x + -2.5 = -2.958039892 Simplifying x + -2.5 = -2.958039892 Reorder the terms: -2.5 + x = -2.958039892 Solving -2.5 + x = -2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.958039892 + 2.5 x = -2.958039892 + 2.5 Combine like terms: -2.958039892 + 2.5 = -0.458039892 x = -0.458039892 Simplifying x = -0.458039892Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.458039892, -0.458039892}
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