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Simplifying 2.6 = x(0.050 + 3x) 2.6 = (0.050 * x + 3x * x) 2.6 = (0.050x + 3x2) Solving 2.6 = 0.050x + 3x2 Solving for variable 'x'. Reorder the terms: 2.6 + -0.050x + -3x2 = 0.050x + -0.050x + 3x2 + -3x2 Combine like terms: 0.050x + -0.050x = 0.000 2.6 + -0.050x + -3x2 = 0.000 + 3x2 + -3x2 2.6 + -0.050x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 2.6 + -0.050x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -0.8666666667 + 0.01666666667x + x2 = 0 Move the constant term to the right: Add '0.8666666667' to each side of the equation. -0.8666666667 + 0.01666666667x + 0.8666666667 + x2 = 0 + 0.8666666667 Reorder the terms: -0.8666666667 + 0.8666666667 + 0.01666666667x + x2 = 0 + 0.8666666667 Combine like terms: -0.8666666667 + 0.8666666667 = 0.0000000000 0.0000000000 + 0.01666666667x + x2 = 0 + 0.8666666667 0.01666666667x + x2 = 0 + 0.8666666667 Combine like terms: 0 + 0.8666666667 = 0.8666666667 0.01666666667x + x2 = 0.8666666667 The x term is 0.01666666667x. Take half its coefficient (0.008333333335). Square it (0.00006944444447) and add it to both sides. Add '0.00006944444447' to each side of the equation. 0.01666666667x + 0.00006944444447 + x2 = 0.8666666667 + 0.00006944444447 Reorder the terms: 0.00006944444447 + 0.01666666667x + x2 = 0.8666666667 + 0.00006944444447 Combine like terms: 0.8666666667 + 0.00006944444447 = 0.86673611114447 0.00006944444447 + 0.01666666667x + x2 = 0.86673611114447 Factor a perfect square on the left side: (x + 0.008333333335)(x + 0.008333333335) = 0.86673611114447 Calculate the square root of the right side: 0.930986633 Break this problem into two subproblems by setting (x + 0.008333333335) equal to 0.930986633 and -0.930986633.Subproblem 1
x + 0.008333333335 = 0.930986633 Simplifying x + 0.008333333335 = 0.930986633 Reorder the terms: 0.008333333335 + x = 0.930986633 Solving 0.008333333335 + x = 0.930986633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.008333333335' to each side of the equation. 0.008333333335 + -0.008333333335 + x = 0.930986633 + -0.008333333335 Combine like terms: 0.008333333335 + -0.008333333335 = 0.000000000000 0.000000000000 + x = 0.930986633 + -0.008333333335 x = 0.930986633 + -0.008333333335 Combine like terms: 0.930986633 + -0.008333333335 = 0.922653299665 x = 0.922653299665 Simplifying x = 0.922653299665Subproblem 2
x + 0.008333333335 = -0.930986633 Simplifying x + 0.008333333335 = -0.930986633 Reorder the terms: 0.008333333335 + x = -0.930986633 Solving 0.008333333335 + x = -0.930986633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.008333333335' to each side of the equation. 0.008333333335 + -0.008333333335 + x = -0.930986633 + -0.008333333335 Combine like terms: 0.008333333335 + -0.008333333335 = 0.000000000000 0.000000000000 + x = -0.930986633 + -0.008333333335 x = -0.930986633 + -0.008333333335 Combine like terms: -0.930986633 + -0.008333333335 = -0.939319966335 x = -0.939319966335 Simplifying x = -0.939319966335Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.922653299665, -0.939319966335}
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