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Simplifying 13x2 + -63x + -30 = 0 Reorder the terms: -30 + -63x + 13x2 = 0 Solving -30 + -63x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -2.307692308 + -4.846153846x + x2 = 0 Move the constant term to the right: Add '2.307692308' to each side of the equation. -2.307692308 + -4.846153846x + 2.307692308 + x2 = 0 + 2.307692308 Reorder the terms: -2.307692308 + 2.307692308 + -4.846153846x + x2 = 0 + 2.307692308 Combine like terms: -2.307692308 + 2.307692308 = 0.000000000 0.000000000 + -4.846153846x + x2 = 0 + 2.307692308 -4.846153846x + x2 = 0 + 2.307692308 Combine like terms: 0 + 2.307692308 = 2.307692308 -4.846153846x + x2 = 2.307692308 The x term is -4.846153846x. Take half its coefficient (-2.423076923). Square it (5.871301775) and add it to both sides. Add '5.871301775' to each side of the equation. -4.846153846x + 5.871301775 + x2 = 2.307692308 + 5.871301775 Reorder the terms: 5.871301775 + -4.846153846x + x2 = 2.307692308 + 5.871301775 Combine like terms: 2.307692308 + 5.871301775 = 8.178994083 5.871301775 + -4.846153846x + x2 = 8.178994083 Factor a perfect square on the left side: (x + -2.423076923)(x + -2.423076923) = 8.178994083 Calculate the square root of the right side: 2.859894068 Break this problem into two subproblems by setting (x + -2.423076923) equal to 2.859894068 and -2.859894068.Subproblem 1
x + -2.423076923 = 2.859894068 Simplifying x + -2.423076923 = 2.859894068 Reorder the terms: -2.423076923 + x = 2.859894068 Solving -2.423076923 + x = 2.859894068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.423076923' to each side of the equation. -2.423076923 + 2.423076923 + x = 2.859894068 + 2.423076923 Combine like terms: -2.423076923 + 2.423076923 = 0.000000000 0.000000000 + x = 2.859894068 + 2.423076923 x = 2.859894068 + 2.423076923 Combine like terms: 2.859894068 + 2.423076923 = 5.282970991 x = 5.282970991 Simplifying x = 5.282970991Subproblem 2
x + -2.423076923 = -2.859894068 Simplifying x + -2.423076923 = -2.859894068 Reorder the terms: -2.423076923 + x = -2.859894068 Solving -2.423076923 + x = -2.859894068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.423076923' to each side of the equation. -2.423076923 + 2.423076923 + x = -2.859894068 + 2.423076923 Combine like terms: -2.423076923 + 2.423076923 = 0.000000000 0.000000000 + x = -2.859894068 + 2.423076923 x = -2.859894068 + 2.423076923 Combine like terms: -2.859894068 + 2.423076923 = -0.436817145 x = -0.436817145 Simplifying x = -0.436817145Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.282970991, -0.436817145}
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