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Simplifying 3x(-4)(5 + -1x) = 7x + 2 Reorder the terms for easier multiplication: 3 * -4x(5 + -1x) = 7x + 2 Multiply 3 * -4 -12x(5 + -1x) = 7x + 2 (5 * -12x + -1x * -12x) = 7x + 2 (-60x + 12x2) = 7x + 2 Reorder the terms: -60x + 12x2 = 2 + 7x Solving -60x + 12x2 = 2 + 7x Solving for variable 'x'. Reorder the terms: -2 + -60x + -7x + 12x2 = 2 + 7x + -2 + -7x Combine like terms: -60x + -7x = -67x -2 + -67x + 12x2 = 2 + 7x + -2 + -7x Reorder the terms: -2 + -67x + 12x2 = 2 + -2 + 7x + -7x Combine like terms: 2 + -2 = 0 -2 + -67x + 12x2 = 0 + 7x + -7x -2 + -67x + 12x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -2 + -67x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.1666666667 + -5.583333333x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -5.583333333x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -5.583333333x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -5.583333333x + x2 = 0 + 0.1666666667 -5.583333333x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -5.583333333x + x2 = 0.1666666667 The x term is -5.583333333x. Take half its coefficient (-2.791666667). Square it (7.793402780) and add it to both sides. Add '7.793402780' to each side of the equation. -5.583333333x + 7.793402780 + x2 = 0.1666666667 + 7.793402780 Reorder the terms: 7.793402780 + -5.583333333x + x2 = 0.1666666667 + 7.793402780 Combine like terms: 0.1666666667 + 7.793402780 = 7.9600694467 7.793402780 + -5.583333333x + x2 = 7.9600694467 Factor a perfect square on the left side: (x + -2.791666667)(x + -2.791666667) = 7.9600694467 Calculate the square root of the right side: 2.821359503 Break this problem into two subproblems by setting (x + -2.791666667) equal to 2.821359503 and -2.821359503.Subproblem 1
x + -2.791666667 = 2.821359503 Simplifying x + -2.791666667 = 2.821359503 Reorder the terms: -2.791666667 + x = 2.821359503 Solving -2.791666667 + x = 2.821359503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.791666667' to each side of the equation. -2.791666667 + 2.791666667 + x = 2.821359503 + 2.791666667 Combine like terms: -2.791666667 + 2.791666667 = 0.000000000 0.000000000 + x = 2.821359503 + 2.791666667 x = 2.821359503 + 2.791666667 Combine like terms: 2.821359503 + 2.791666667 = 5.61302617 x = 5.61302617 Simplifying x = 5.61302617Subproblem 2
x + -2.791666667 = -2.821359503 Simplifying x + -2.791666667 = -2.821359503 Reorder the terms: -2.791666667 + x = -2.821359503 Solving -2.791666667 + x = -2.821359503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.791666667' to each side of the equation. -2.791666667 + 2.791666667 + x = -2.821359503 + 2.791666667 Combine like terms: -2.791666667 + 2.791666667 = 0.000000000 0.000000000 + x = -2.821359503 + 2.791666667 x = -2.821359503 + 2.791666667 Combine like terms: -2.821359503 + 2.791666667 = -0.029692836 x = -0.029692836 Simplifying x = -0.029692836Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.61302617, -0.029692836}
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