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Simplifying x(x + 3.6) = 20.77 Reorder the terms: x(3.6 + x) = 20.77 (3.6 * x + x * x) = 20.77 (3.6x + x2) = 20.77 Solving 3.6x + x2 = 20.77 Solving for variable 'x'. Reorder the terms: -20.77 + 3.6x + x2 = 20.77 + -20.77 Combine like terms: 20.77 + -20.77 = 0.00 -20.77 + 3.6x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '20.77' to each side of the equation. -20.77 + 3.6x + 20.77 + x2 = 0.00 + 20.77 Reorder the terms: -20.77 + 20.77 + 3.6x + x2 = 0.00 + 20.77 Combine like terms: -20.77 + 20.77 = 0.00 0.00 + 3.6x + x2 = 0.00 + 20.77 3.6x + x2 = 0.00 + 20.77 Combine like terms: 0.00 + 20.77 = 20.77 3.6x + x2 = 20.77 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = 20.77 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 20.77 + 3.24 Combine like terms: 20.77 + 3.24 = 24.01 3.24 + 3.6x + x2 = 24.01 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 24.01 Calculate the square root of the right side: 4.9 Break this problem into two subproblems by setting (x + 1.8) equal to 4.9 and -4.9.Subproblem 1
x + 1.8 = 4.9 Simplifying x + 1.8 = 4.9 Reorder the terms: 1.8 + x = 4.9 Solving 1.8 + x = 4.9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 4.9 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 4.9 + -1.8 x = 4.9 + -1.8 Combine like terms: 4.9 + -1.8 = 3.1 x = 3.1 Simplifying x = 3.1Subproblem 2
x + 1.8 = -4.9 Simplifying x + 1.8 = -4.9 Reorder the terms: 1.8 + x = -4.9 Solving 1.8 + x = -4.9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -4.9 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -4.9 + -1.8 x = -4.9 + -1.8 Combine like terms: -4.9 + -1.8 = -6.7 x = -6.7 Simplifying x = -6.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1, -6.7}
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