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Simplifying 0 = 2.5x2 + -6x + -8 Reorder the terms: 0 = -8 + -6x + 2.5x2 Solving 0 = -8 + -6x + 2.5x2 Solving for variable 'x'. Combine like terms: 0 + 8 = 8 8 + 6x + -2.5x2 = -8 + -6x + 2.5x2 + 8 + 6x + -2.5x2 Reorder the terms: 8 + 6x + -2.5x2 = -8 + 8 + -6x + 6x + 2.5x2 + -2.5x2 Combine like terms: -8 + 8 = 0 8 + 6x + -2.5x2 = 0 + -6x + 6x + 2.5x2 + -2.5x2 8 + 6x + -2.5x2 = -6x + 6x + 2.5x2 + -2.5x2 Combine like terms: -6x + 6x = 0 8 + 6x + -2.5x2 = 0 + 2.5x2 + -2.5x2 8 + 6x + -2.5x2 = 2.5x2 + -2.5x2 Combine like terms: 2.5x2 + -2.5x2 = 0.0 8 + 6x + -2.5x2 = 0.0 Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. -3.2 + -2.4x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -2.4x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -2.4x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -2.4x + x2 = 0 + 3.2 -2.4x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -2.4x + x2 = 3.2 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 3.2 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 3.2 + 1.44 Combine like terms: 3.2 + 1.44 = 4.64 1.44 + -2.4x + x2 = 4.64 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 4.64 Calculate the square root of the right side: 2.154065923 Break this problem into two subproblems by setting (x + -1.2) equal to 2.154065923 and -2.154065923.Subproblem 1
x + -1.2 = 2.154065923 Simplifying x + -1.2 = 2.154065923 Reorder the terms: -1.2 + x = 2.154065923 Solving -1.2 + x = 2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 2.154065923 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 2.154065923 + 1.2 x = 2.154065923 + 1.2 Combine like terms: 2.154065923 + 1.2 = 3.354065923 x = 3.354065923 Simplifying x = 3.354065923Subproblem 2
x + -1.2 = -2.154065923 Simplifying x + -1.2 = -2.154065923 Reorder the terms: -1.2 + x = -2.154065923 Solving -1.2 + x = -2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -2.154065923 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -2.154065923 + 1.2 x = -2.154065923 + 1.2 Combine like terms: -2.154065923 + 1.2 = -0.954065923 x = -0.954065923 Simplifying x = -0.954065923Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.354065923, -0.954065923}
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