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Simplifying 3(2x + 6) + -5(x + 8) * x + -22 = 0 Reorder the terms: 3(6 + 2x) + -5(x + 8) * x + -22 = 0 (6 * 3 + 2x * 3) + -5(x + 8) * x + -22 = 0 (18 + 6x) + -5(x + 8) * x + -22 = 0 Reorder the terms: 18 + 6x + -5(8 + x) * x + -22 = 0 Reorder the terms for easier multiplication: 18 + 6x + -5x(8 + x) + -22 = 0 18 + 6x + (8 * -5x + x * -5x) + -22 = 0 18 + 6x + (-40x + -5x2) + -22 = 0 Reorder the terms: 18 + -22 + 6x + -40x + -5x2 = 0 Combine like terms: 18 + -22 = -4 -4 + 6x + -40x + -5x2 = 0 Combine like terms: 6x + -40x = -34x -4 + -34x + -5x2 = 0 Solving -4 + -34x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 34x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 34x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + 34x + 5x2 = 0 Solving 4 + 34x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 6.8x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 6.8x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 6.8x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 6.8x + x2 = 0 + -0.8 6.8x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 6.8x + x2 = -0.8 The x term is 6.8x. Take half its coefficient (3.4). Square it (11.56) and add it to both sides. Add '11.56' to each side of the equation. 6.8x + 11.56 + x2 = -0.8 + 11.56 Reorder the terms: 11.56 + 6.8x + x2 = -0.8 + 11.56 Combine like terms: -0.8 + 11.56 = 10.76 11.56 + 6.8x + x2 = 10.76 Factor a perfect square on the left side: (x + 3.4)(x + 3.4) = 10.76 Calculate the square root of the right side: 3.280243893 Break this problem into two subproblems by setting (x + 3.4) equal to 3.280243893 and -3.280243893.Subproblem 1
x + 3.4 = 3.280243893 Simplifying x + 3.4 = 3.280243893 Reorder the terms: 3.4 + x = 3.280243893 Solving 3.4 + x = 3.280243893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + x = 3.280243893 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = 3.280243893 + -3.4 x = 3.280243893 + -3.4 Combine like terms: 3.280243893 + -3.4 = -0.119756107 x = -0.119756107 Simplifying x = -0.119756107Subproblem 2
x + 3.4 = -3.280243893 Simplifying x + 3.4 = -3.280243893 Reorder the terms: 3.4 + x = -3.280243893 Solving 3.4 + x = -3.280243893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.4' to each side of the equation. 3.4 + -3.4 + x = -3.280243893 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + x = -3.280243893 + -3.4 x = -3.280243893 + -3.4 Combine like terms: -3.280243893 + -3.4 = -6.680243893 x = -6.680243893 Simplifying x = -6.680243893Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.119756107, -6.680243893}Solution
x = {-0.119756107, -6.680243893}
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