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Simplifying -6(4x + 1) + 7x + 9x(x + -3) = 4 Reorder the terms: -6(1 + 4x) + 7x + 9x(x + -3) = 4 (1 * -6 + 4x * -6) + 7x + 9x(x + -3) = 4 (-6 + -24x) + 7x + 9x(x + -3) = 4 Reorder the terms: -6 + -24x + 7x + 9x(-3 + x) = 4 -6 + -24x + 7x + (-3 * 9x + x * 9x) = 4 -6 + -24x + 7x + (-27x + 9x2) = 4 Combine like terms: -24x + 7x = -17x -6 + -17x + -27x + 9x2 = 4 Combine like terms: -17x + -27x = -44x -6 + -44x + 9x2 = 4 Solving -6 + -44x + 9x2 = 4 Solving for variable 'x'. Reorder the terms: -6 + -4 + -44x + 9x2 = 4 + -4 Combine like terms: -6 + -4 = -10 -10 + -44x + 9x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -10 + -44x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + -4.888888889x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -4.888888889x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -4.888888889x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -4.888888889x + x2 = 0 + 1.111111111 -4.888888889x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -4.888888889x + x2 = 1.111111111 The x term is -4.888888889x. Take half its coefficient (-2.444444445). Square it (5.975308645) and add it to both sides. Add '5.975308645' to each side of the equation. -4.888888889x + 5.975308645 + x2 = 1.111111111 + 5.975308645 Reorder the terms: 5.975308645 + -4.888888889x + x2 = 1.111111111 + 5.975308645 Combine like terms: 1.111111111 + 5.975308645 = 7.086419756 5.975308645 + -4.888888889x + x2 = 7.086419756 Factor a perfect square on the left side: (x + -2.444444445)(x + -2.444444445) = 7.086419756 Calculate the square root of the right side: 2.662033012 Break this problem into two subproblems by setting (x + -2.444444445) equal to 2.662033012 and -2.662033012.Subproblem 1
x + -2.444444445 = 2.662033012 Simplifying x + -2.444444445 = 2.662033012 Reorder the terms: -2.444444445 + x = 2.662033012 Solving -2.444444445 + x = 2.662033012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.444444445' to each side of the equation. -2.444444445 + 2.444444445 + x = 2.662033012 + 2.444444445 Combine like terms: -2.444444445 + 2.444444445 = 0.000000000 0.000000000 + x = 2.662033012 + 2.444444445 x = 2.662033012 + 2.444444445 Combine like terms: 2.662033012 + 2.444444445 = 5.106477457 x = 5.106477457 Simplifying x = 5.106477457Subproblem 2
x + -2.444444445 = -2.662033012 Simplifying x + -2.444444445 = -2.662033012 Reorder the terms: -2.444444445 + x = -2.662033012 Solving -2.444444445 + x = -2.662033012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.444444445' to each side of the equation. -2.444444445 + 2.444444445 + x = -2.662033012 + 2.444444445 Combine like terms: -2.444444445 + 2.444444445 = 0.000000000 0.000000000 + x = -2.662033012 + 2.444444445 x = -2.662033012 + 2.444444445 Combine like terms: -2.662033012 + 2.444444445 = -0.217588567 x = -0.217588567 Simplifying x = -0.217588567Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.106477457, -0.217588567}
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