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Simplifying (0.7x + 3)(6x + -0.6) = 0 Reorder the terms: (3 + 0.7x)(6x + -0.6) = 0 Reorder the terms: (3 + 0.7x)(-0.6 + 6x) = 0 Multiply (3 + 0.7x) * (-0.6 + 6x) (3(-0.6 + 6x) + 0.7x * (-0.6 + 6x)) = 0 ((-0.6 * 3 + 6x * 3) + 0.7x * (-0.6 + 6x)) = 0 ((-1.8 + 18x) + 0.7x * (-0.6 + 6x)) = 0 (-1.8 + 18x + (-0.6 * 0.7x + 6x * 0.7x)) = 0 (-1.8 + 18x + (-0.42x + 4.2x2)) = 0 Combine like terms: 18x + -0.42x = 17.58x (-1.8 + 17.58x + 4.2x2) = 0 Solving -1.8 + 17.58x + 4.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.2 the coefficient of the squared term: Divide each side by '4.2'. -0.4285714286 + 4.185714286x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 4.185714286x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 4.185714286x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 4.185714286x + x2 = 0 + 0.4285714286 4.185714286x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 4.185714286x + x2 = 0.4285714286 The x term is 4.185714286x. Take half its coefficient (2.092857143). Square it (4.380051021) and add it to both sides. Add '4.380051021' to each side of the equation. 4.185714286x + 4.380051021 + x2 = 0.4285714286 + 4.380051021 Reorder the terms: 4.380051021 + 4.185714286x + x2 = 0.4285714286 + 4.380051021 Combine like terms: 0.4285714286 + 4.380051021 = 4.8086224496 4.380051021 + 4.185714286x + x2 = 4.8086224496 Factor a perfect square on the left side: (x + 2.092857143)(x + 2.092857143) = 4.8086224496 Calculate the square root of the right side: 2.192857143 Break this problem into two subproblems by setting (x + 2.092857143) equal to 2.192857143 and -2.192857143.Subproblem 1
x + 2.092857143 = 2.192857143 Simplifying x + 2.092857143 = 2.192857143 Reorder the terms: 2.092857143 + x = 2.192857143 Solving 2.092857143 + x = 2.192857143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.092857143' to each side of the equation. 2.092857143 + -2.092857143 + x = 2.192857143 + -2.092857143 Combine like terms: 2.092857143 + -2.092857143 = 0.000000000 0.000000000 + x = 2.192857143 + -2.092857143 x = 2.192857143 + -2.092857143 Combine like terms: 2.192857143 + -2.092857143 = 0.1 x = 0.1 Simplifying x = 0.1Subproblem 2
x + 2.092857143 = -2.192857143 Simplifying x + 2.092857143 = -2.192857143 Reorder the terms: 2.092857143 + x = -2.192857143 Solving 2.092857143 + x = -2.192857143 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.092857143' to each side of the equation. 2.092857143 + -2.092857143 + x = -2.192857143 + -2.092857143 Combine like terms: 2.092857143 + -2.092857143 = 0.000000000 0.000000000 + x = -2.192857143 + -2.092857143 x = -2.192857143 + -2.092857143 Combine like terms: -2.192857143 + -2.092857143 = -4.285714286 x = -4.285714286 Simplifying x = -4.285714286Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1, -4.285714286}
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