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Simplifying 26x2 + 102x + -6 = 0 Reorder the terms: -6 + 102x + 26x2 = 0 Solving -6 + 102x + 26x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 51x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 51x + 13x2)' equal to zero and attempt to solve: Simplifying -3 + 51x + 13x2 = 0 Solving -3 + 51x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.2307692308 + 3.923076923x + x2 = 0 Move the constant term to the right: Add '0.2307692308' to each side of the equation. -0.2307692308 + 3.923076923x + 0.2307692308 + x2 = 0 + 0.2307692308 Reorder the terms: -0.2307692308 + 0.2307692308 + 3.923076923x + x2 = 0 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + 3.923076923x + x2 = 0 + 0.2307692308 3.923076923x + x2 = 0 + 0.2307692308 Combine like terms: 0 + 0.2307692308 = 0.2307692308 3.923076923x + x2 = 0.2307692308 The x term is 3.923076923x. Take half its coefficient (1.961538462). Square it (3.847633138) and add it to both sides. Add '3.847633138' to each side of the equation. 3.923076923x + 3.847633138 + x2 = 0.2307692308 + 3.847633138 Reorder the terms: 3.847633138 + 3.923076923x + x2 = 0.2307692308 + 3.847633138 Combine like terms: 0.2307692308 + 3.847633138 = 4.0784023688 3.847633138 + 3.923076923x + x2 = 4.0784023688 Factor a perfect square on the left side: (x + 1.961538462)(x + 1.961538462) = 4.0784023688 Calculate the square root of the right side: 2.019505476 Break this problem into two subproblems by setting (x + 1.961538462) equal to 2.019505476 and -2.019505476.Subproblem 1
x + 1.961538462 = 2.019505476 Simplifying x + 1.961538462 = 2.019505476 Reorder the terms: 1.961538462 + x = 2.019505476 Solving 1.961538462 + x = 2.019505476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.961538462' to each side of the equation. 1.961538462 + -1.961538462 + x = 2.019505476 + -1.961538462 Combine like terms: 1.961538462 + -1.961538462 = 0.000000000 0.000000000 + x = 2.019505476 + -1.961538462 x = 2.019505476 + -1.961538462 Combine like terms: 2.019505476 + -1.961538462 = 0.057967014 x = 0.057967014 Simplifying x = 0.057967014Subproblem 2
x + 1.961538462 = -2.019505476 Simplifying x + 1.961538462 = -2.019505476 Reorder the terms: 1.961538462 + x = -2.019505476 Solving 1.961538462 + x = -2.019505476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.961538462' to each side of the equation. 1.961538462 + -1.961538462 + x = -2.019505476 + -1.961538462 Combine like terms: 1.961538462 + -1.961538462 = 0.000000000 0.000000000 + x = -2.019505476 + -1.961538462 x = -2.019505476 + -1.961538462 Combine like terms: -2.019505476 + -1.961538462 = -3.981043938 x = -3.981043938 Simplifying x = -3.981043938Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.057967014, -3.981043938}Solution
x = {0.057967014, -3.981043938}
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