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Simplifying 40x + -1x * x = 60 Multiply x * x 40x + -1x2 = 60 Solving 40x + -1x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + 40x + -1x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 40x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 60 + -40x + x2 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + -40x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -40x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -40x + x2 = 0 + -60 -40x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -40x + x2 = -60 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -60 + 400 Reorder the terms: 400 + -40x + x2 = -60 + 400 Combine like terms: -60 + 400 = 340 400 + -40x + x2 = 340 Factor a perfect square on the left side: (x + -20)(x + -20) = 340 Calculate the square root of the right side: 18.439088915 Break this problem into two subproblems by setting (x + -20) equal to 18.439088915 and -18.439088915.Subproblem 1
x + -20 = 18.439088915 Simplifying x + -20 = 18.439088915 Reorder the terms: -20 + x = 18.439088915 Solving -20 + x = 18.439088915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 18.439088915 + 20 Combine like terms: -20 + 20 = 0 0 + x = 18.439088915 + 20 x = 18.439088915 + 20 Combine like terms: 18.439088915 + 20 = 38.439088915 x = 38.439088915 Simplifying x = 38.439088915Subproblem 2
x + -20 = -18.439088915 Simplifying x + -20 = -18.439088915 Reorder the terms: -20 + x = -18.439088915 Solving -20 + x = -18.439088915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -18.439088915 + 20 Combine like terms: -20 + 20 = 0 0 + x = -18.439088915 + 20 x = -18.439088915 + 20 Combine like terms: -18.439088915 + 20 = 1.560911085 x = 1.560911085 Simplifying x = 1.560911085Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.439088915, 1.560911085}
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