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Simplifying 56 + -1(3x + -14) = 3x(x + 7) + x Reorder the terms: 56 + -1(-14 + 3x) = 3x(x + 7) + x 56 + (-14 * -1 + 3x * -1) = 3x(x + 7) + x 56 + (14 + -3x) = 3x(x + 7) + x Combine like terms: 56 + 14 = 70 70 + -3x = 3x(x + 7) + x Reorder the terms: 70 + -3x = 3x(7 + x) + x 70 + -3x = (7 * 3x + x * 3x) + x 70 + -3x = (21x + 3x2) + x Reorder the terms: 70 + -3x = 21x + x + 3x2 Combine like terms: 21x + x = 22x 70 + -3x = 22x + 3x2 Solving 70 + -3x = 22x + 3x2 Solving for variable 'x'. Combine like terms: -3x + -22x = -25x 70 + -25x + -3x2 = 22x + 3x2 + -22x + -3x2 Reorder the terms: 70 + -25x + -3x2 = 22x + -22x + 3x2 + -3x2 Combine like terms: 22x + -22x = 0 70 + -25x + -3x2 = 0 + 3x2 + -3x2 70 + -25x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 70 + -25x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -23.33333333 + 8.333333333x + x2 = 0 Move the constant term to the right: Add '23.33333333' to each side of the equation. -23.33333333 + 8.333333333x + 23.33333333 + x2 = 0 + 23.33333333 Reorder the terms: -23.33333333 + 23.33333333 + 8.333333333x + x2 = 0 + 23.33333333 Combine like terms: -23.33333333 + 23.33333333 = 0.00000000 0.00000000 + 8.333333333x + x2 = 0 + 23.33333333 8.333333333x + x2 = 0 + 23.33333333 Combine like terms: 0 + 23.33333333 = 23.33333333 8.333333333x + x2 = 23.33333333 The x term is 8.333333333x. Take half its coefficient (4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. 8.333333333x + 17.36111111 + x2 = 23.33333333 + 17.36111111 Reorder the terms: 17.36111111 + 8.333333333x + x2 = 23.33333333 + 17.36111111 Combine like terms: 23.33333333 + 17.36111111 = 40.69444444 17.36111111 + 8.333333333x + x2 = 40.69444444 Factor a perfect square on the left side: (x + 4.166666667)(x + 4.166666667) = 40.69444444 Calculate the square root of the right side: 6.379219736 Break this problem into two subproblems by setting (x + 4.166666667) equal to 6.379219736 and -6.379219736.Subproblem 1
x + 4.166666667 = 6.379219736 Simplifying x + 4.166666667 = 6.379219736 Reorder the terms: 4.166666667 + x = 6.379219736 Solving 4.166666667 + x = 6.379219736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = 6.379219736 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = 6.379219736 + -4.166666667 x = 6.379219736 + -4.166666667 Combine like terms: 6.379219736 + -4.166666667 = 2.212553069 x = 2.212553069 Simplifying x = 2.212553069Subproblem 2
x + 4.166666667 = -6.379219736 Simplifying x + 4.166666667 = -6.379219736 Reorder the terms: 4.166666667 + x = -6.379219736 Solving 4.166666667 + x = -6.379219736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.166666667' to each side of the equation. 4.166666667 + -4.166666667 + x = -6.379219736 + -4.166666667 Combine like terms: 4.166666667 + -4.166666667 = 0.000000000 0.000000000 + x = -6.379219736 + -4.166666667 x = -6.379219736 + -4.166666667 Combine like terms: -6.379219736 + -4.166666667 = -10.545886403 x = -10.545886403 Simplifying x = -10.545886403Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.212553069, -10.545886403}
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