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Simplifying x2 + -4x = 26 Reorder the terms: -4x + x2 = 26 Solving -4x + x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + -4x + x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -4x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -4x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -4x + x2 = 0 + 26 -4x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -4x + x2 = 26 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 26 + 4 Reorder the terms: 4 + -4x + x2 = 26 + 4 Combine like terms: 26 + 4 = 30 4 + -4x + x2 = 30 Factor a perfect square on the left side: (x + -2)(x + -2) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + -2) equal to 5.477225575 and -5.477225575.Subproblem 1
x + -2 = 5.477225575 Simplifying x + -2 = 5.477225575 Reorder the terms: -2 + x = 5.477225575 Solving -2 + x = 5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.477225575 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.477225575 + 2 x = 5.477225575 + 2 Combine like terms: 5.477225575 + 2 = 7.477225575 x = 7.477225575 Simplifying x = 7.477225575Subproblem 2
x + -2 = -5.477225575 Simplifying x + -2 = -5.477225575 Reorder the terms: -2 + x = -5.477225575 Solving -2 + x = -5.477225575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.477225575 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.477225575 + 2 x = -5.477225575 + 2 Combine like terms: -5.477225575 + 2 = -3.477225575 x = -3.477225575 Simplifying x = -3.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.477225575, -3.477225575}
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