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Simplifying x2 + -2x = 20.085 Reorder the terms: -2x + x2 = 20.085 Solving -2x + x2 = 20.085 Solving for variable 'x'. Reorder the terms: -20.085 + -2x + x2 = 20.085 + -20.085 Combine like terms: 20.085 + -20.085 = 0.000 -20.085 + -2x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '20.085' to each side of the equation. -20.085 + -2x + 20.085 + x2 = 0.000 + 20.085 Reorder the terms: -20.085 + 20.085 + -2x + x2 = 0.000 + 20.085 Combine like terms: -20.085 + 20.085 = 0.000 0.000 + -2x + x2 = 0.000 + 20.085 -2x + x2 = 0.000 + 20.085 Combine like terms: 0.000 + 20.085 = 20.085 -2x + x2 = 20.085 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 20.085 + 1 Reorder the terms: 1 + -2x + x2 = 20.085 + 1 Combine like terms: 20.085 + 1 = 21.085 1 + -2x + x2 = 21.085 Factor a perfect square on the left side: (x + -1)(x + -1) = 21.085 Calculate the square root of the right side: 4.59184059 Break this problem into two subproblems by setting (x + -1) equal to 4.59184059 and -4.59184059.Subproblem 1
x + -1 = 4.59184059 Simplifying x + -1 = 4.59184059 Reorder the terms: -1 + x = 4.59184059 Solving -1 + x = 4.59184059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.59184059 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.59184059 + 1 x = 4.59184059 + 1 Combine like terms: 4.59184059 + 1 = 5.59184059 x = 5.59184059 Simplifying x = 5.59184059Subproblem 2
x + -1 = -4.59184059 Simplifying x + -1 = -4.59184059 Reorder the terms: -1 + x = -4.59184059 Solving -1 + x = -4.59184059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.59184059 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.59184059 + 1 x = -4.59184059 + 1 Combine like terms: -4.59184059 + 1 = -3.59184059 x = -3.59184059 Simplifying x = -3.59184059Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.59184059, -3.59184059}
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