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Simplifying 3(2x + -3)(x + 1) + -2(3 + -1x) * 2 + 5(x + -3)(x + 3) = 0 Reorder the terms: 3(-3 + 2x)(x + 1) + -2(3 + -1x) * 2 + 5(x + -3)(x + 3) = 0 Reorder the terms: 3(-3 + 2x)(1 + x) + -2(3 + -1x) * 2 + 5(x + -3)(x + 3) = 0 Multiply (-3 + 2x) * (1 + x) 3(-3(1 + x) + 2x * (1 + x)) + -2(3 + -1x) * 2 + 5(x + -3)(x + 3) = 0 3((1 * -3 + x * -3) + 2x * (1 + x)) + -2(3 + -1x) * 2 + 5(x + -3)(x + 3) = 0 3((-3 + -3x) + 2x * (1 + x)) + -2(3 + -1x) * 2 + 5(x + -3)(x + 3) = 0 3(-3 + -3x + (1 * 2x + x * 2x)) + -2(3 + -1x) * 2 + 5(x + -3)(x + 3) = 0 3(-3 + -3x + (2x + 2x2)) + -2(3 + -1x) * 2 + 5(x + -3)(x + 3) = 0 Combine like terms: -3x + 2x = -1x 3(-3 + -1x + 2x2) + -2(3 + -1x) * 2 + 5(x + -3)(x + 3) = 0 (-3 * 3 + -1x * 3 + 2x2 * 3) + -2(3 + -1x) * 2 + 5(x + -3)(x + 3) = 0 (-9 + -3x + 6x2) + -2(3 + -1x) * 2 + 5(x + -3)(x + 3) = 0 Reorder the terms for easier multiplication: -9 + -3x + 6x2 + -2 * 2(3 + -1x) + 5(x + -3)(x + 3) = 0 Multiply -2 * 2 -9 + -3x + 6x2 + -4(3 + -1x) + 5(x + -3)(x + 3) = 0 -9 + -3x + 6x2 + (3 * -4 + -1x * -4) + 5(x + -3)(x + 3) = 0 -9 + -3x + 6x2 + (-12 + 4x) + 5(x + -3)(x + 3) = 0 Reorder the terms: -9 + -3x + 6x2 + -12 + 4x + 5(-3 + x)(x + 3) = 0 Reorder the terms: -9 + -3x + 6x2 + -12 + 4x + 5(-3 + x)(3 + x) = 0 Multiply (-3 + x) * (3 + x) -9 + -3x + 6x2 + -12 + 4x + 5(-3(3 + x) + x(3 + x)) = 0 -9 + -3x + 6x2 + -12 + 4x + 5((3 * -3 + x * -3) + x(3 + x)) = 0 -9 + -3x + 6x2 + -12 + 4x + 5((-9 + -3x) + x(3 + x)) = 0 -9 + -3x + 6x2 + -12 + 4x + 5(-9 + -3x + (3 * x + x * x)) = 0 -9 + -3x + 6x2 + -12 + 4x + 5(-9 + -3x + (3x + x2)) = 0 Combine like terms: -3x + 3x = 0 -9 + -3x + 6x2 + -12 + 4x + 5(-9 + 0 + x2) = 0 -9 + -3x + 6x2 + -12 + 4x + 5(-9 + x2) = 0 -9 + -3x + 6x2 + -12 + 4x + (-9 * 5 + x2 * 5) = 0 -9 + -3x + 6x2 + -12 + 4x + (-45 + 5x2) = 0 Reorder the terms: -9 + -12 + -45 + -3x + 4x + 6x2 + 5x2 = 0 Combine like terms: -9 + -12 = -21 -21 + -45 + -3x + 4x + 6x2 + 5x2 = 0 Combine like terms: -21 + -45 = -66 -66 + -3x + 4x + 6x2 + 5x2 = 0 Combine like terms: -3x + 4x = 1x -66 + 1x + 6x2 + 5x2 = 0 Combine like terms: 6x2 + 5x2 = 11x2 -66 + 1x + 11x2 = 0 Solving -66 + 1x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -6 + 0.09090909091x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 0.09090909091x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 0.09090909091x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 0.09090909091x + x2 = 0 + 6 0.09090909091x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 0.09090909091x + x2 = 6 The x term is 0.09090909091x. Take half its coefficient (0.04545454546). Square it (0.002066115703) and add it to both sides. Add '0.002066115703' to each side of the equation. 0.09090909091x + 0.002066115703 + x2 = 6 + 0.002066115703 Reorder the terms: 0.002066115703 + 0.09090909091x + x2 = 6 + 0.002066115703 Combine like terms: 6 + 0.002066115703 = 6.002066115703 0.002066115703 + 0.09090909091x + x2 = 6.002066115703 Factor a perfect square on the left side: (x + 0.04545454546)(x + 0.04545454546) = 6.002066115703 Calculate the square root of the right side: 2.449911451 Break this problem into two subproblems by setting (x + 0.04545454546) equal to 2.449911451 and -2.449911451.Subproblem 1
x + 0.04545454546 = 2.449911451 Simplifying x + 0.04545454546 = 2.449911451 Reorder the terms: 0.04545454546 + x = 2.449911451 Solving 0.04545454546 + x = 2.449911451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04545454546' to each side of the equation. 0.04545454546 + -0.04545454546 + x = 2.449911451 + -0.04545454546 Combine like terms: 0.04545454546 + -0.04545454546 = 0.00000000000 0.00000000000 + x = 2.449911451 + -0.04545454546 x = 2.449911451 + -0.04545454546 Combine like terms: 2.449911451 + -0.04545454546 = 2.40445690554 x = 2.40445690554 Simplifying x = 2.40445690554Subproblem 2
x + 0.04545454546 = -2.449911451 Simplifying x + 0.04545454546 = -2.449911451 Reorder the terms: 0.04545454546 + x = -2.449911451 Solving 0.04545454546 + x = -2.449911451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04545454546' to each side of the equation. 0.04545454546 + -0.04545454546 + x = -2.449911451 + -0.04545454546 Combine like terms: 0.04545454546 + -0.04545454546 = 0.00000000000 0.00000000000 + x = -2.449911451 + -0.04545454546 x = -2.449911451 + -0.04545454546 Combine like terms: -2.449911451 + -0.04545454546 = -2.49536599646 x = -2.49536599646 Simplifying x = -2.49536599646Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.40445690554, -2.49536599646}
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