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Simplifying 40x + -1x2 = 50 Solving 40x + -1x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 40x + -1x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 40x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 50 + -40x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -40x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -40x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -40x + x2 = 0 + -50 -40x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -40x + x2 = -50 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 = -50 + 400 Reorder the terms: 400 + -40x + x2 = -50 + 400 Combine like terms: -50 + 400 = 350 400 + -40x + x2 = 350 Factor a perfect square on the left side: (x + -20)(x + -20) = 350 Calculate the square root of the right side: 18.708286934 Break this problem into two subproblems by setting (x + -20) equal to 18.708286934 and -18.708286934.Subproblem 1
x + -20 = 18.708286934 Simplifying x + -20 = 18.708286934 Reorder the terms: -20 + x = 18.708286934 Solving -20 + x = 18.708286934 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 = 18.708286934 + 20 Combine like terms: -20 + 20 = 0 0 + x = 18.708286934 + 20 x = 18.708286934 + 20 Combine like terms: 18.708286934 + 20 = 38.708286934 x = 38.708286934 Simplifying x = 38.708286934Subproblem 2
x + -20 = -18.708286934 Simplifying x + -20 = -18.708286934 Reorder the terms: -20 + x = -18.708286934 Solving -20 + x = -18.708286934 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 = -18.708286934 + 20 Combine like terms: -20 + 20 = 0 0 + x = -18.708286934 + 20 x = -18.708286934 + 20 Combine like terms: -18.708286934 + 20 = 1.291713066 x = 1.291713066 Simplifying x = 1.291713066Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.708286934, 1.291713066}
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