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Simplifying 0 = x2 + -40x + -320 Reorder the terms: 0 = -320 + -40x + x2 Solving 0 = -320 + -40x + x2 Solving for variable 'x'. Combine like terms: 0 + 320 = 320 320 + 40x + -1x2 = -320 + -40x + x2 + 320 + 40x + -1x2 Reorder the terms: 320 + 40x + -1x2 = -320 + 320 + -40x + 40x + x2 + -1x2 Combine like terms: -320 + 320 = 0 320 + 40x + -1x2 = 0 + -40x + 40x + x2 + -1x2 320 + 40x + -1x2 = -40x + 40x + x2 + -1x2 Combine like terms: -40x + 40x = 0 320 + 40x + -1x2 = 0 + x2 + -1x2 320 + 40x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 320 + 40x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -320 + -40x + x2 = 0 Move the constant term to the right: Add '320' to each side of the equation. -320 + -40x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + -40x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + -40x + x2 = 0 + 320 -40x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 -40x + x2 = 320 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 = 320 + 400 Reorder the terms: 400 + -40x + x2 = 320 + 400 Combine like terms: 320 + 400 = 720 400 + -40x + x2 = 720 Factor a perfect square on the left side: (x + -20)(x + -20) = 720 Calculate the square root of the right side: 26.83281573 Break this problem into two subproblems by setting (x + -20) equal to 26.83281573 and -26.83281573.Subproblem 1
x + -20 = 26.83281573 Simplifying x + -20 = 26.83281573 Reorder the terms: -20 + x = 26.83281573 Solving -20 + x = 26.83281573 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 = 26.83281573 + 20 Combine like terms: -20 + 20 = 0 0 + x = 26.83281573 + 20 x = 26.83281573 + 20 Combine like terms: 26.83281573 + 20 = 46.83281573 x = 46.83281573 Simplifying x = 46.83281573Subproblem 2
x + -20 = -26.83281573 Simplifying x + -20 = -26.83281573 Reorder the terms: -20 + x = -26.83281573 Solving -20 + x = -26.83281573 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 = -26.83281573 + 20 Combine like terms: -20 + 20 = 0 0 + x = -26.83281573 + 20 x = -26.83281573 + 20 Combine like terms: -26.83281573 + 20 = -6.83281573 x = -6.83281573 Simplifying x = -6.83281573Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.83281573, -6.83281573}
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