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Simplifying x(x + -40) = 8 Reorder the terms: x(-40 + x) = 8 (-40 * x + x * x) = 8 (-40x + x2) = 8 Solving -40x + x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -40x + x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -40x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -40x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -40x + x2 = 0 + 8 -40x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -40x + x2 = 8 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 = 8 + 400 Reorder the terms: 400 + -40x + x2 = 8 + 400 Combine like terms: 8 + 400 = 408 400 + -40x + x2 = 408 Factor a perfect square on the left side: (x + -20)(x + -20) = 408 Calculate the square root of the right side: 20.199009877 Break this problem into two subproblems by setting (x + -20) equal to 20.199009877 and -20.199009877.Subproblem 1
x + -20 = 20.199009877 Simplifying x + -20 = 20.199009877 Reorder the terms: -20 + x = 20.199009877 Solving -20 + x = 20.199009877 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 = 20.199009877 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.199009877 + 20 x = 20.199009877 + 20 Combine like terms: 20.199009877 + 20 = 40.199009877 x = 40.199009877 Simplifying x = 40.199009877Subproblem 2
x + -20 = -20.199009877 Simplifying x + -20 = -20.199009877 Reorder the terms: -20 + x = -20.199009877 Solving -20 + x = -20.199009877 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 = -20.199009877 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.199009877 + 20 x = -20.199009877 + 20 Combine like terms: -20.199009877 + 20 = -0.199009877 x = -0.199009877 Simplifying x = -0.199009877Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.199009877, -0.199009877}
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