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Simplifying 1.8 = -5x2 + -10x + 20 Reorder the terms: 1.8 = 20 + -10x + -5x2 Solving 1.8 = 20 + -10x + -5x2 Solving for variable 'x'. Combine like terms: 1.8 + -20 = -18.2 -18.2 + 10x + 5x2 = 20 + -10x + -5x2 + -20 + 10x + 5x2 Reorder the terms: -18.2 + 10x + 5x2 = 20 + -20 + -10x + 10x + -5x2 + 5x2 Combine like terms: 20 + -20 = 0 -18.2 + 10x + 5x2 = 0 + -10x + 10x + -5x2 + 5x2 -18.2 + 10x + 5x2 = -10x + 10x + -5x2 + 5x2 Combine like terms: -10x + 10x = 0 -18.2 + 10x + 5x2 = 0 + -5x2 + 5x2 -18.2 + 10x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -18.2 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.64 + 2x + x2 = 0 Move the constant term to the right: Add '3.64' to each side of the equation. -3.64 + 2x + 3.64 + x2 = 0 + 3.64 Reorder the terms: -3.64 + 3.64 + 2x + x2 = 0 + 3.64 Combine like terms: -3.64 + 3.64 = 0.00 0.00 + 2x + x2 = 0 + 3.64 2x + x2 = 0 + 3.64 Combine like terms: 0 + 3.64 = 3.64 2x + x2 = 3.64 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 3.64 + 1 Reorder the terms: 1 + 2x + x2 = 3.64 + 1 Combine like terms: 3.64 + 1 = 4.64 1 + 2x + x2 = 4.64 Factor a perfect square on the left side: (x + 1)(x + 1) = 4.64 Calculate the square root of the right side: 2.154065923 Break this problem into two subproblems by setting (x + 1) equal to 2.154065923 and -2.154065923.Subproblem 1
x + 1 = 2.154065923 Simplifying x + 1 = 2.154065923 Reorder the terms: 1 + x = 2.154065923 Solving 1 + x = 2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.154065923 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.154065923 + -1 x = 2.154065923 + -1 Combine like terms: 2.154065923 + -1 = 1.154065923 x = 1.154065923 Simplifying x = 1.154065923Subproblem 2
x + 1 = -2.154065923 Simplifying x + 1 = -2.154065923 Reorder the terms: 1 + x = -2.154065923 Solving 1 + x = -2.154065923 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.154065923 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.154065923 + -1 x = -2.154065923 + -1 Combine like terms: -2.154065923 + -1 = -3.154065923 x = -3.154065923 Simplifying x = -3.154065923Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.154065923, -3.154065923}
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