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Simplifying 6x(-11 + -2x) = 4x + -3 (-11 * 6x + -2x * 6x) = 4x + -3 (-66x + -12x2) = 4x + -3 Reorder the terms: -66x + -12x2 = -3 + 4x Solving -66x + -12x2 = -3 + 4x Solving for variable 'x'. Reorder the terms: 3 + -66x + -4x + -12x2 = -3 + 4x + 3 + -4x Combine like terms: -66x + -4x = -70x 3 + -70x + -12x2 = -3 + 4x + 3 + -4x Reorder the terms: 3 + -70x + -12x2 = -3 + 3 + 4x + -4x Combine like terms: -3 + 3 = 0 3 + -70x + -12x2 = 0 + 4x + -4x 3 + -70x + -12x2 = 4x + -4x Combine like terms: 4x + -4x = 0 3 + -70x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.25 + 5.833333333x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 5.833333333x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 5.833333333x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 5.833333333x + x2 = 0 + 0.25 5.833333333x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 5.833333333x + x2 = 0.25 The x term is 5.833333333x. Take half its coefficient (2.916666667). Square it (8.506944446) and add it to both sides. Add '8.506944446' to each side of the equation. 5.833333333x + 8.506944446 + x2 = 0.25 + 8.506944446 Reorder the terms: 8.506944446 + 5.833333333x + x2 = 0.25 + 8.506944446 Combine like terms: 0.25 + 8.506944446 = 8.756944446 8.506944446 + 5.833333333x + x2 = 8.756944446 Factor a perfect square on the left side: (x + 2.916666667)(x + 2.916666667) = 8.756944446 Calculate the square root of the right side: 2.959213484 Break this problem into two subproblems by setting (x + 2.916666667) equal to 2.959213484 and -2.959213484.Subproblem 1
x + 2.916666667 = 2.959213484 Simplifying x + 2.916666667 = 2.959213484 Reorder the terms: 2.916666667 + x = 2.959213484 Solving 2.916666667 + x = 2.959213484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.916666667' to each side of the equation. 2.916666667 + -2.916666667 + x = 2.959213484 + -2.916666667 Combine like terms: 2.916666667 + -2.916666667 = 0.000000000 0.000000000 + x = 2.959213484 + -2.916666667 x = 2.959213484 + -2.916666667 Combine like terms: 2.959213484 + -2.916666667 = 0.042546817 x = 0.042546817 Simplifying x = 0.042546817Subproblem 2
x + 2.916666667 = -2.959213484 Simplifying x + 2.916666667 = -2.959213484 Reorder the terms: 2.916666667 + x = -2.959213484 Solving 2.916666667 + x = -2.959213484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.916666667' to each side of the equation. 2.916666667 + -2.916666667 + x = -2.959213484 + -2.916666667 Combine like terms: 2.916666667 + -2.916666667 = 0.000000000 0.000000000 + x = -2.959213484 + -2.916666667 x = -2.959213484 + -2.916666667 Combine like terms: -2.959213484 + -2.916666667 = -5.875880151 x = -5.875880151 Simplifying x = -5.875880151Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.042546817, -5.875880151}
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