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Simplifying 6x2 + x + -15 = 8 Reorder the terms: -15 + x + 6x2 = 8 Solving -15 + x + 6x2 = 8 Solving for variable 'x'. Reorder the terms: -15 + -8 + x + 6x2 = 8 + -8 Combine like terms: -15 + -8 = -23 -23 + x + 6x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -23 + x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.833333333 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '3.833333333' to each side of the equation. -3.833333333 + 0.1666666667x + 3.833333333 + x2 = 0 + 3.833333333 Reorder the terms: -3.833333333 + 3.833333333 + 0.1666666667x + x2 = 0 + 3.833333333 Combine like terms: -3.833333333 + 3.833333333 = 0.000000000 0.000000000 + 0.1666666667x + x2 = 0 + 3.833333333 0.1666666667x + x2 = 0 + 3.833333333 Combine like terms: 0 + 3.833333333 = 3.833333333 0.1666666667x + x2 = 3.833333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1666666667x + 0.25 + x2 = 3.833333333 + 0.25 Reorder the terms: 0.25 + 0.1666666667x + x2 = 3.833333333 + 0.25 Combine like terms: 3.833333333 + 0.25 = 4.083333333 0.25 + 0.1666666667x + x2 = 4.083333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.083333333 Calculate the square root of the right side: 2.020725942 Break this problem into two subproblems by setting (x + 0.5) equal to 2.020725942 and -2.020725942.Subproblem 1
x + 0.5 = 2.020725942 Simplifying x + 0.5 = 2.020725942 Reorder the terms: 0.5 + x = 2.020725942 Solving 0.5 + x = 2.020725942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.020725942 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.020725942 + -0.5 x = 2.020725942 + -0.5 Combine like terms: 2.020725942 + -0.5 = 1.520725942 x = 1.520725942 Simplifying x = 1.520725942Subproblem 2
x + 0.5 = -2.020725942 Simplifying x + 0.5 = -2.020725942 Reorder the terms: 0.5 + x = -2.020725942 Solving 0.5 + x = -2.020725942 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.020725942 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.020725942 + -0.5 x = -2.020725942 + -0.5 Combine like terms: -2.020725942 + -0.5 = -2.520725942 x = -2.520725942 Simplifying x = -2.520725942Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.520725942, -2.520725942}
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