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Simplifying 6x2 + -1x = 98 Reorder the terms: -1x + 6x2 = 98 Solving -1x + 6x2 = 98 Solving for variable 'x'. Reorder the terms: -98 + -1x + 6x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + -1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -16.33333333 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '16.33333333' to each side of the equation. -16.33333333 + -0.1666666667x + 16.33333333 + x2 = 0 + 16.33333333 Reorder the terms: -16.33333333 + 16.33333333 + -0.1666666667x + x2 = 0 + 16.33333333 Combine like terms: -16.33333333 + 16.33333333 = 0.00000000 0.00000000 + -0.1666666667x + x2 = 0 + 16.33333333 -0.1666666667x + x2 = 0 + 16.33333333 Combine like terms: 0 + 16.33333333 = 16.33333333 -0.1666666667x + x2 = 16.33333333 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 16.33333333 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 16.33333333 + 0.006944444447 Combine like terms: 16.33333333 + 0.006944444447 = 16.340277774447 0.006944444447 + -0.1666666667x + x2 = 16.340277774447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 16.340277774447 Calculate the square root of the right side: 4.042310945 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 4.042310945 and -4.042310945.Subproblem 1
x + -0.08333333335 = 4.042310945 Simplifying x + -0.08333333335 = 4.042310945 Reorder the terms: -0.08333333335 + x = 4.042310945 Solving -0.08333333335 + x = 4.042310945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 4.042310945 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 4.042310945 + 0.08333333335 x = 4.042310945 + 0.08333333335 Combine like terms: 4.042310945 + 0.08333333335 = 4.12564427835 x = 4.12564427835 Simplifying x = 4.12564427835Subproblem 2
x + -0.08333333335 = -4.042310945 Simplifying x + -0.08333333335 = -4.042310945 Reorder the terms: -0.08333333335 + x = -4.042310945 Solving -0.08333333335 + x = -4.042310945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -4.042310945 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -4.042310945 + 0.08333333335 x = -4.042310945 + 0.08333333335 Combine like terms: -4.042310945 + 0.08333333335 = -3.95897761165 x = -3.95897761165 Simplifying x = -3.95897761165Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.12564427835, -3.95897761165}
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