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Simplifying 2 = 0.8x2 + 1.8x Reorder the terms: 2 = 1.8x + 0.8x2 Solving 2 = 1.8x + 0.8x2 Solving for variable 'x'. Reorder the terms: 2 + -1.8x + -0.8x2 = 1.8x + -1.8x + 0.8x2 + -0.8x2 Combine like terms: 1.8x + -1.8x = 0.0 2 + -1.8x + -0.8x2 = 0.0 + 0.8x2 + -0.8x2 2 + -1.8x + -0.8x2 = 0.8x2 + -0.8x2 Combine like terms: 0.8x2 + -0.8x2 = 0.0 2 + -1.8x + -0.8x2 = 0.0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. -2.5 + 2.25x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 2.25x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 2.25x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 2.25x + x2 = 0 + 2.5 2.25x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 2.25x + x2 = 2.5 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 2.5 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 2.5 + 1.265625 Combine like terms: 2.5 + 1.265625 = 3.765625 1.265625 + 2.25x + x2 = 3.765625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (x + 1.125) equal to 1.940521837 and -1.940521837.Subproblem 1
x + 1.125 = 1.940521837 Simplifying x + 1.125 = 1.940521837 Reorder the terms: 1.125 + x = 1.940521837 Solving 1.125 + x = 1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 1.940521837 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.940521837 + -1.125 x = 1.940521837 + -1.125 Combine like terms: 1.940521837 + -1.125 = 0.815521837 x = 0.815521837 Simplifying x = 0.815521837Subproblem 2
x + 1.125 = -1.940521837 Simplifying x + 1.125 = -1.940521837 Reorder the terms: 1.125 + x = -1.940521837 Solving 1.125 + x = -1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -1.940521837 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.940521837 + -1.125 x = -1.940521837 + -1.125 Combine like terms: -1.940521837 + -1.125 = -3.065521837 x = -3.065521837 Simplifying x = -3.065521837Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.815521837, -3.065521837}
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