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Simplifying 0 = x2 + 4x + -26 Reorder the terms: 0 = -26 + 4x + x2 Solving 0 = -26 + 4x + x2 Solving for variable 'x'. Combine like terms: 0 + 26 = 26 26 + -4x + -1x2 = -26 + 4x + x2 + 26 + -4x + -1x2 Reorder the terms: 26 + -4x + -1x2 = -26 + 26 + 4x + -4x + x2 + -1x2 Combine like terms: -26 + 26 = 0 26 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2 26 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 26 + -4x + -1x2 = 0 + x2 + -1x2 26 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 26 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -26 + 4x + x2 = 0 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 = 3.477225575 x = 3.477225575 Simplifying x = 3.477225575Subproblem 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 = -7.477225575 x = -7.477225575 Simplifying x = -7.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.477225575, -7.477225575}
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