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Simplifying 4x + -1(9 + -3x) * 8x = 1 Reorder the terms for easier multiplication: 4x + -1 * 8x(9 + -3x) = 1 Multiply -1 * 8 4x + -8x(9 + -3x) = 1 4x + (9 * -8x + -3x * -8x) = 1 4x + (-72x + 24x2) = 1 Combine like terms: 4x + -72x = -68x -68x + 24x2 = 1 Solving -68x + 24x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -68x + 24x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -68x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.04166666667 + -2.833333333x + x2 = 0 Move the constant term to the right: Add '0.04166666667' to each side of the equation. -0.04166666667 + -2.833333333x + 0.04166666667 + x2 = 0 + 0.04166666667 Reorder the terms: -0.04166666667 + 0.04166666667 + -2.833333333x + x2 = 0 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + -2.833333333x + x2 = 0 + 0.04166666667 -2.833333333x + x2 = 0 + 0.04166666667 Combine like terms: 0 + 0.04166666667 = 0.04166666667 -2.833333333x + x2 = 0.04166666667 The x term is -2.833333333x. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333x + 2.006944445 + x2 = 0.04166666667 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333x + x2 = 0.04166666667 + 2.006944445 Combine like terms: 0.04166666667 + 2.006944445 = 2.04861111167 2.006944445 + -2.833333333x + x2 = 2.04861111167 Factor a perfect square on the left side: (x + -1.416666667)(x + -1.416666667) = 2.04861111167 Calculate the square root of the right side: 1.431297003 Break this problem into two subproblems by setting (x + -1.416666667) equal to 1.431297003 and -1.431297003.Subproblem 1
x + -1.416666667 = 1.431297003 Simplifying x + -1.416666667 = 1.431297003 Reorder the terms: -1.416666667 + x = 1.431297003 Solving -1.416666667 + x = 1.431297003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = 1.431297003 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = 1.431297003 + 1.416666667 x = 1.431297003 + 1.416666667 Combine like terms: 1.431297003 + 1.416666667 = 2.84796367 x = 2.84796367 Simplifying x = 2.84796367Subproblem 2
x + -1.416666667 = -1.431297003 Simplifying x + -1.416666667 = -1.431297003 Reorder the terms: -1.416666667 + x = -1.431297003 Solving -1.416666667 + x = -1.431297003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = -1.431297003 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = -1.431297003 + 1.416666667 x = -1.431297003 + 1.416666667 Combine like terms: -1.431297003 + 1.416666667 = -0.014630336 x = -0.014630336 Simplifying x = -0.014630336Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.84796367, -0.014630336}
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