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Simplifying -21x2 + 95x + 6 = 0 Reorder the terms: 6 + 95x + -21x2 = 0 Solving 6 + 95x + -21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. -0.2857142857 + -4.523809524x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -4.523809524x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -4.523809524x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -4.523809524x + x2 = 0 + 0.2857142857 -4.523809524x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -4.523809524x + x2 = 0.2857142857 The x term is -4.523809524x. Take half its coefficient (-2.261904762). Square it (5.116213152) and add it to both sides. Add '5.116213152' to each side of the equation. -4.523809524x + 5.116213152 + x2 = 0.2857142857 + 5.116213152 Reorder the terms: 5.116213152 + -4.523809524x + x2 = 0.2857142857 + 5.116213152 Combine like terms: 0.2857142857 + 5.116213152 = 5.4019274377 5.116213152 + -4.523809524x + x2 = 5.4019274377 Factor a perfect square on the left side: (x + -2.261904762)(x + -2.261904762) = 5.4019274377 Calculate the square root of the right side: 2.324204689 Break this problem into two subproblems by setting (x + -2.261904762) equal to 2.324204689 and -2.324204689.Subproblem 1
x + -2.261904762 = 2.324204689 Simplifying x + -2.261904762 = 2.324204689 Reorder the terms: -2.261904762 + x = 2.324204689 Solving -2.261904762 + x = 2.324204689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.261904762' to each side of the equation. -2.261904762 + 2.261904762 + x = 2.324204689 + 2.261904762 Combine like terms: -2.261904762 + 2.261904762 = 0.000000000 0.000000000 + x = 2.324204689 + 2.261904762 x = 2.324204689 + 2.261904762 Combine like terms: 2.324204689 + 2.261904762 = 4.586109451 x = 4.586109451 Simplifying x = 4.586109451Subproblem 2
x + -2.261904762 = -2.324204689 Simplifying x + -2.261904762 = -2.324204689 Reorder the terms: -2.261904762 + x = -2.324204689 Solving -2.261904762 + x = -2.324204689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.261904762' to each side of the equation. -2.261904762 + 2.261904762 + x = -2.324204689 + 2.261904762 Combine like terms: -2.261904762 + 2.261904762 = 0.000000000 0.000000000 + x = -2.324204689 + 2.261904762 x = -2.324204689 + 2.261904762 Combine like terms: -2.324204689 + 2.261904762 = -0.062299927 x = -0.062299927 Simplifying x = -0.062299927Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.586109451, -0.062299927}
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