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Simplifying (0.6x + -1.28)(18x + 8) = 0 Reorder the terms: (-1.28 + 0.6x)(18x + 8) = 0 Reorder the terms: (-1.28 + 0.6x)(8 + 18x) = 0 Multiply (-1.28 + 0.6x) * (8 + 18x) (-1.28(8 + 18x) + 0.6x * (8 + 18x)) = 0 ((8 * -1.28 + 18x * -1.28) + 0.6x * (8 + 18x)) = 0 ((-10.24 + -23.04x) + 0.6x * (8 + 18x)) = 0 (-10.24 + -23.04x + (8 * 0.6x + 18x * 0.6x)) = 0 (-10.24 + -23.04x + (4.8x + 10.8x2)) = 0 Combine like terms: -23.04x + 4.8x = -18.24x (-10.24 + -18.24x + 10.8x2) = 0 Solving -10.24 + -18.24x + 10.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10.8 the coefficient of the squared term: Divide each side by '10.8'. -0.9481481481 + -1.688888889x + x2 = 0 Move the constant term to the right: Add '0.9481481481' to each side of the equation. -0.9481481481 + -1.688888889x + 0.9481481481 + x2 = 0 + 0.9481481481 Reorder the terms: -0.9481481481 + 0.9481481481 + -1.688888889x + x2 = 0 + 0.9481481481 Combine like terms: -0.9481481481 + 0.9481481481 = 0.0000000000 0.0000000000 + -1.688888889x + x2 = 0 + 0.9481481481 -1.688888889x + x2 = 0 + 0.9481481481 Combine like terms: 0 + 0.9481481481 = 0.9481481481 -1.688888889x + x2 = 0.9481481481 The x term is -1.688888889x. Take half its coefficient (-0.8444444445). Square it (0.7130864198) and add it to both sides. Add '0.7130864198' to each side of the equation. -1.688888889x + 0.7130864198 + x2 = 0.9481481481 + 0.7130864198 Reorder the terms: 0.7130864198 + -1.688888889x + x2 = 0.9481481481 + 0.7130864198 Combine like terms: 0.9481481481 + 0.7130864198 = 1.6612345679 0.7130864198 + -1.688888889x + x2 = 1.6612345679 Factor a perfect square on the left side: (x + -0.8444444445)(x + -0.8444444445) = 1.6612345679 Calculate the square root of the right side: 1.288888889 Break this problem into two subproblems by setting (x + -0.8444444445) equal to 1.288888889 and -1.288888889.Subproblem 1
x + -0.8444444445 = 1.288888889 Simplifying x + -0.8444444445 = 1.288888889 Reorder the terms: -0.8444444445 + x = 1.288888889 Solving -0.8444444445 + x = 1.288888889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8444444445' to each side of the equation. -0.8444444445 + 0.8444444445 + x = 1.288888889 + 0.8444444445 Combine like terms: -0.8444444445 + 0.8444444445 = 0.0000000000 0.0000000000 + x = 1.288888889 + 0.8444444445 x = 1.288888889 + 0.8444444445 Combine like terms: 1.288888889 + 0.8444444445 = 2.1333333335 x = 2.1333333335 Simplifying x = 2.1333333335Subproblem 2
x + -0.8444444445 = -1.288888889 Simplifying x + -0.8444444445 = -1.288888889 Reorder the terms: -0.8444444445 + x = -1.288888889 Solving -0.8444444445 + x = -1.288888889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8444444445' to each side of the equation. -0.8444444445 + 0.8444444445 + x = -1.288888889 + 0.8444444445 Combine like terms: -0.8444444445 + 0.8444444445 = 0.0000000000 0.0000000000 + x = -1.288888889 + 0.8444444445 x = -1.288888889 + 0.8444444445 Combine like terms: -1.288888889 + 0.8444444445 = -0.4444444445 x = -0.4444444445 Simplifying x = -0.4444444445Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1333333335, -0.4444444445}
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