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Simplifying 0 = x2 + 26x + 4 Reorder the terms: 0 = 4 + 26x + x2 Solving 0 = 4 + 26x + x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -26x + -1x2 = 4 + 26x + x2 + -4 + -26x + -1x2 Reorder the terms: -4 + -26x + -1x2 = 4 + -4 + 26x + -26x + x2 + -1x2 Combine like terms: 4 + -4 = 0 -4 + -26x + -1x2 = 0 + 26x + -26x + x2 + -1x2 -4 + -26x + -1x2 = 26x + -26x + x2 + -1x2 Combine like terms: 26x + -26x = 0 -4 + -26x + -1x2 = 0 + x2 + -1x2 -4 + -26x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4 + -26x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 26x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 26x + x2)' equal to zero and attempt to solve: Simplifying 4 + 26x + x2 = 0 Solving 4 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 26x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 26x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 26x + x2 = 0 + -4 26x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 26x + x2 = -4 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -4 + 169 Reorder the terms: 169 + 26x + x2 = -4 + 169 Combine like terms: -4 + 169 = 165 169 + 26x + x2 = 165 Factor a perfect square on the left side: (x + 13)(x + 13) = 165 Calculate the square root of the right side: 12.845232579 Break this problem into two subproblems by setting (x + 13) equal to 12.845232579 and -12.845232579.Subproblem 1
x + 13 = 12.845232579 Simplifying x + 13 = 12.845232579 Reorder the terms: 13 + x = 12.845232579 Solving 13 + x = 12.845232579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 12.845232579 + -13 Combine like terms: 13 + -13 = 0 0 + x = 12.845232579 + -13 x = 12.845232579 + -13 Combine like terms: 12.845232579 + -13 = -0.154767421 x = -0.154767421 Simplifying x = -0.154767421Subproblem 2
x + 13 = -12.845232579 Simplifying x + 13 = -12.845232579 Reorder the terms: 13 + x = -12.845232579 Solving 13 + x = -12.845232579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -12.845232579 + -13 Combine like terms: 13 + -13 = 0 0 + x = -12.845232579 + -13 x = -12.845232579 + -13 Combine like terms: -12.845232579 + -13 = -25.845232579 x = -25.845232579 Simplifying x = -25.845232579Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.154767421, -25.845232579}Solution
x = {-0.154767421, -25.845232579}
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