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Simplifying 5x2 + -8x + -5 = 15 Reorder the terms: -5 + -8x + 5x2 = 15 Solving -5 + -8x + 5x2 = 15 Solving for variable 'x'. Reorder the terms: -5 + -15 + -8x + 5x2 = 15 + -15 Combine like terms: -5 + -15 = -20 -20 + -8x + 5x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -20 + -8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + -1.6x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.6x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1.6x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.6x + x2 = 0 + 4 -1.6x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.6x + x2 = 4 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 4 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 4 + 0.64 Combine like terms: 4 + 0.64 = 4.64 0.64 + -1.6x + x2 = 4.64 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 4.64 Calculate the square root of the right side: 2.154065923 Break this problem into two subproblems by setting (x + -0.8) equal to 2.154065923 and -2.154065923.Subproblem 1
x + -0.8 = 2.154065923 Simplifying x + -0.8 = 2.154065923 Reorder the terms: -0.8 + x = 2.154065923 Solving -0.8 + x = 2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 2.154065923 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 2.154065923 + 0.8 x = 2.154065923 + 0.8 Combine like terms: 2.154065923 + 0.8 = 2.954065923 x = 2.954065923 Simplifying x = 2.954065923Subproblem 2
x + -0.8 = -2.154065923 Simplifying x + -0.8 = -2.154065923 Reorder the terms: -0.8 + x = -2.154065923 Solving -0.8 + x = -2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -2.154065923 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -2.154065923 + 0.8 x = -2.154065923 + 0.8 Combine like terms: -2.154065923 + 0.8 = -1.354065923 x = -1.354065923 Simplifying x = -1.354065923Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.954065923, -1.354065923}
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