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Simplifying 22 = 6x * 6x + -5x + -21 Reorder the terms for easier multiplication: 22 = 6 * 6x * x + -5x + -21 Multiply 6 * 6 22 = 36x * x + -5x + -21 Multiply x * x 22 = 36x2 + -5x + -21 Reorder the terms: 22 = -21 + -5x + 36x2 Solving 22 = -21 + -5x + 36x2 Solving for variable 'x'. Combine like terms: 22 + 21 = 43 43 + 5x + -36x2 = -21 + -5x + 36x2 + 21 + 5x + -36x2 Reorder the terms: 43 + 5x + -36x2 = -21 + 21 + -5x + 5x + 36x2 + -36x2 Combine like terms: -21 + 21 = 0 43 + 5x + -36x2 = 0 + -5x + 5x + 36x2 + -36x2 43 + 5x + -36x2 = -5x + 5x + 36x2 + -36x2 Combine like terms: -5x + 5x = 0 43 + 5x + -36x2 = 0 + 36x2 + -36x2 43 + 5x + -36x2 = 36x2 + -36x2 Combine like terms: 36x2 + -36x2 = 0 43 + 5x + -36x2 = 0 Begin completing the square. Divide all terms by -36 the coefficient of the squared term: Divide each side by '-36'. -1.194444444 + -0.1388888889x + x2 = 0 Move the constant term to the right: Add '1.194444444' to each side of the equation. -1.194444444 + -0.1388888889x + 1.194444444 + x2 = 0 + 1.194444444 Reorder the terms: -1.194444444 + 1.194444444 + -0.1388888889x + x2 = 0 + 1.194444444 Combine like terms: -1.194444444 + 1.194444444 = 0.000000000 0.000000000 + -0.1388888889x + x2 = 0 + 1.194444444 -0.1388888889x + x2 = 0 + 1.194444444 Combine like terms: 0 + 1.194444444 = 1.194444444 -0.1388888889x + x2 = 1.194444444 The x term is -0.1388888889x. Take half its coefficient (-0.06944444445). Square it (0.004822530865) and add it to both sides. Add '0.004822530865' to each side of the equation. -0.1388888889x + 0.004822530865 + x2 = 1.194444444 + 0.004822530865 Reorder the terms: 0.004822530865 + -0.1388888889x + x2 = 1.194444444 + 0.004822530865 Combine like terms: 1.194444444 + 0.004822530865 = 1.199266974865 0.004822530865 + -0.1388888889x + x2 = 1.199266974865 Factor a perfect square on the left side: (x + -0.06944444445)(x + -0.06944444445) = 1.199266974865 Calculate the square root of the right side: 1.095110485 Break this problem into two subproblems by setting (x + -0.06944444445) equal to 1.095110485 and -1.095110485.Subproblem 1
x + -0.06944444445 = 1.095110485 Simplifying x + -0.06944444445 = 1.095110485 Reorder the terms: -0.06944444445 + x = 1.095110485 Solving -0.06944444445 + x = 1.095110485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06944444445' to each side of the equation. -0.06944444445 + 0.06944444445 + x = 1.095110485 + 0.06944444445 Combine like terms: -0.06944444445 + 0.06944444445 = 0.00000000000 0.00000000000 + x = 1.095110485 + 0.06944444445 x = 1.095110485 + 0.06944444445 Combine like terms: 1.095110485 + 0.06944444445 = 1.16455492945 x = 1.16455492945 Simplifying x = 1.16455492945Subproblem 2
x + -0.06944444445 = -1.095110485 Simplifying x + -0.06944444445 = -1.095110485 Reorder the terms: -0.06944444445 + x = -1.095110485 Solving -0.06944444445 + x = -1.095110485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06944444445' to each side of the equation. -0.06944444445 + 0.06944444445 + x = -1.095110485 + 0.06944444445 Combine like terms: -0.06944444445 + 0.06944444445 = 0.00000000000 0.00000000000 + x = -1.095110485 + 0.06944444445 x = -1.095110485 + 0.06944444445 Combine like terms: -1.095110485 + 0.06944444445 = -1.02566604055 x = -1.02566604055 Simplifying x = -1.02566604055Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.16455492945, -1.02566604055}
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