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Simplifying x2 + -40x + 400 = 709 Reorder the terms: 400 + -40x + x2 = 709 Solving 400 + -40x + x2 = 709 Solving for variable 'x'. Reorder the terms: 400 + -709 + -40x + x2 = 709 + -709 Combine like terms: 400 + -709 = -309 -309 + -40x + x2 = 709 + -709 Combine like terms: 709 + -709 = 0 -309 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '309' to each side of the equation. -309 + -40x + 309 + x2 = 0 + 309 Reorder the terms: -309 + 309 + -40x + x2 = 0 + 309 Combine like terms: -309 + 309 = 0 0 + -40x + x2 = 0 + 309 -40x + x2 = 0 + 309 Combine like terms: 0 + 309 = 309 -40x + x2 = 309 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 = 309 + 400 Reorder the terms: 400 + -40x + x2 = 309 + 400 Combine like terms: 309 + 400 = 709 400 + -40x + x2 = 709 Factor a perfect square on the left side: (x + -20)(x + -20) = 709 Calculate the square root of the right side: 26.627053911 Break this problem into two subproblems by setting (x + -20) equal to 26.627053911 and -26.627053911.Subproblem 1
x + -20 = 26.627053911 Simplifying x + -20 = 26.627053911 Reorder the terms: -20 + x = 26.627053911 Solving -20 + x = 26.627053911 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 = 26.627053911 + 20 Combine like terms: -20 + 20 = 0 0 + x = 26.627053911 + 20 x = 26.627053911 + 20 Combine like terms: 26.627053911 + 20 = 46.627053911 x = 46.627053911 Simplifying x = 46.627053911Subproblem 2
x + -20 = -26.627053911 Simplifying x + -20 = -26.627053911 Reorder the terms: -20 + x = -26.627053911 Solving -20 + x = -26.627053911 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 = -26.627053911 + 20 Combine like terms: -20 + 20 = 0 0 + x = -26.627053911 + 20 x = -26.627053911 + 20 Combine like terms: -26.627053911 + 20 = -6.627053911 x = -6.627053911 Simplifying x = -6.627053911Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.627053911, -6.627053911}
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