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Simplifying 32.87(0.08 + -1x) = 1.50 + 1.50x(0.08 + -1x) (0.08 * 32.87 + -1x * 32.87) = 1.50 + 1.50x(0.08 + -1x) (2.6296 + -32.87x) = 1.50 + 1.50x(0.08 + -1x) 2.6296 + -32.87x = 1.50 + (0.08 * 1.50x + -1x * 1.50x) 2.6296 + -32.87x = 1.50 + (0.12x + -1.5x2) Solving 2.6296 + -32.87x = 1.50 + 0.12x + -1.5x2 Solving for variable 'x'. Reorder the terms: 2.6296 + -1.50 + -32.87x + -0.12x + 1.5x2 = 1.50 + 0.12x + -1.5x2 + -1.50 + -0.12x + 1.5x2 Combine like terms: 2.6296 + -1.50 = 1.1296 1.1296 + -32.87x + -0.12x + 1.5x2 = 1.50 + 0.12x + -1.5x2 + -1.50 + -0.12x + 1.5x2 Combine like terms: -32.87x + -0.12x = -32.99x 1.1296 + -32.99x + 1.5x2 = 1.50 + 0.12x + -1.5x2 + -1.50 + -0.12x + 1.5x2 Reorder the terms: 1.1296 + -32.99x + 1.5x2 = 1.50 + -1.50 + 0.12x + -0.12x + -1.5x2 + 1.5x2 Combine like terms: 1.50 + -1.50 = 0.00 1.1296 + -32.99x + 1.5x2 = 0.00 + 0.12x + -0.12x + -1.5x2 + 1.5x2 1.1296 + -32.99x + 1.5x2 = 0.12x + -0.12x + -1.5x2 + 1.5x2 Combine like terms: 0.12x + -0.12x = 0.00 1.1296 + -32.99x + 1.5x2 = 0.00 + -1.5x2 + 1.5x2 1.1296 + -32.99x + 1.5x2 = -1.5x2 + 1.5x2 Combine like terms: -1.5x2 + 1.5x2 = 0.0 1.1296 + -32.99x + 1.5x2 = 0.0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. 0.7530666667 + -21.99333333x + x2 = 0 Move the constant term to the right: Add '-0.7530666667' to each side of the equation. 0.7530666667 + -21.99333333x + -0.7530666667 + x2 = 0 + -0.7530666667 Reorder the terms: 0.7530666667 + -0.7530666667 + -21.99333333x + x2 = 0 + -0.7530666667 Combine like terms: 0.7530666667 + -0.7530666667 = 0.0000000000 0.0000000000 + -21.99333333x + x2 = 0 + -0.7530666667 -21.99333333x + x2 = 0 + -0.7530666667 Combine like terms: 0 + -0.7530666667 = -0.7530666667 -21.99333333x + x2 = -0.7530666667 The x term is -21.99333333x. Take half its coefficient (-10.99666667). Square it (120.9266779) and add it to both sides. Add '120.9266779' to each side of the equation. -21.99333333x + 120.9266779 + x2 = -0.7530666667 + 120.9266779 Reorder the terms: 120.9266779 + -21.99333333x + x2 = -0.7530666667 + 120.9266779 Combine like terms: -0.7530666667 + 120.9266779 = 120.1736112333 120.9266779 + -21.99333333x + x2 = 120.1736112333 Factor a perfect square on the left side: (x + -10.99666667)(x + -10.99666667) = 120.1736112333 Calculate the square root of the right side: 10.962372518 Break this problem into two subproblems by setting (x + -10.99666667) equal to 10.962372518 and -10.962372518.Subproblem 1
x + -10.99666667 = 10.962372518 Simplifying x + -10.99666667 = 10.962372518 Reorder the terms: -10.99666667 + x = 10.962372518 Solving -10.99666667 + x = 10.962372518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.99666667' to each side of the equation. -10.99666667 + 10.99666667 + x = 10.962372518 + 10.99666667 Combine like terms: -10.99666667 + 10.99666667 = 0.00000000 0.00000000 + x = 10.962372518 + 10.99666667 x = 10.962372518 + 10.99666667 Combine like terms: 10.962372518 + 10.99666667 = 21.959039188 x = 21.959039188 Simplifying x = 21.959039188Subproblem 2
x + -10.99666667 = -10.962372518 Simplifying x + -10.99666667 = -10.962372518 Reorder the terms: -10.99666667 + x = -10.962372518 Solving -10.99666667 + x = -10.962372518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.99666667' to each side of the equation. -10.99666667 + 10.99666667 + x = -10.962372518 + 10.99666667 Combine like terms: -10.99666667 + 10.99666667 = 0.00000000 0.00000000 + x = -10.962372518 + 10.99666667 x = -10.962372518 + 10.99666667 Combine like terms: -10.962372518 + 10.99666667 = 0.034294152 x = 0.034294152 Simplifying x = 0.034294152Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.959039188, 0.034294152}
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