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Simplifying x2 + -44x = -65 Reorder the terms: -44x + x2 = -65 Solving -44x + x2 = -65 Solving for variable 'x'. Reorder the terms: 65 + -44x + x2 = -65 + 65 Combine like terms: -65 + 65 = 0 65 + -44x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-65' to each side of the equation. 65 + -44x + -65 + x2 = 0 + -65 Reorder the terms: 65 + -65 + -44x + x2 = 0 + -65 Combine like terms: 65 + -65 = 0 0 + -44x + x2 = 0 + -65 -44x + x2 = 0 + -65 Combine like terms: 0 + -65 = -65 -44x + x2 = -65 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = -65 + 484 Reorder the terms: 484 + -44x + x2 = -65 + 484 Combine like terms: -65 + 484 = 419 484 + -44x + x2 = 419 Factor a perfect square on the left side: (x + -22)(x + -22) = 419 Calculate the square root of the right side: 20.46948949 Break this problem into two subproblems by setting (x + -22) equal to 20.46948949 and -20.46948949.Subproblem 1
x + -22 = 20.46948949 Simplifying x + -22 = 20.46948949 Reorder the terms: -22 + x = 20.46948949 Solving -22 + x = 20.46948949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 20.46948949 + 22 Combine like terms: -22 + 22 = 0 0 + x = 20.46948949 + 22 x = 20.46948949 + 22 Combine like terms: 20.46948949 + 22 = 42.46948949 x = 42.46948949 Simplifying x = 42.46948949Subproblem 2
x + -22 = -20.46948949 Simplifying x + -22 = -20.46948949 Reorder the terms: -22 + x = -20.46948949 Solving -22 + x = -20.46948949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -20.46948949 + 22 Combine like terms: -22 + 22 = 0 0 + x = -20.46948949 + 22 x = -20.46948949 + 22 Combine like terms: -20.46948949 + 22 = 1.53051051 x = 1.53051051 Simplifying x = 1.53051051Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.46948949, 1.53051051}
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