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Simplifying 26x2 + 14x + -3 = 0 Reorder the terms: -3 + 14x + 26x2 = 0 Solving -3 + 14x + 26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. -0.1153846154 + 0.5384615385x + x2 = 0 Move the constant term to the right: Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.5384615385x + 0.1153846154 + x2 = 0 + 0.1153846154 Reorder the terms: -0.1153846154 + 0.1153846154 + 0.5384615385x + x2 = 0 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + 0.5384615385x + x2 = 0 + 0.1153846154 0.5384615385x + x2 = 0 + 0.1153846154 Combine like terms: 0 + 0.1153846154 = 0.1153846154 0.5384615385x + x2 = 0.1153846154 The x term is 0.5384615385x. Take half its coefficient (0.2692307693). Square it (0.07248520714) and add it to both sides. Add '0.07248520714' to each side of the equation. 0.5384615385x + 0.07248520714 + x2 = 0.1153846154 + 0.07248520714 Reorder the terms: 0.07248520714 + 0.5384615385x + x2 = 0.1153846154 + 0.07248520714 Combine like terms: 0.1153846154 + 0.07248520714 = 0.18786982254 0.07248520714 + 0.5384615385x + x2 = 0.18786982254 Factor a perfect square on the left side: (x + 0.2692307693)(x + 0.2692307693) = 0.18786982254 Calculate the square root of the right side: 0.433439526 Break this problem into two subproblems by setting (x + 0.2692307693) equal to 0.433439526 and -0.433439526.Subproblem 1
x + 0.2692307693 = 0.433439526 Simplifying x + 0.2692307693 = 0.433439526 Reorder the terms: 0.2692307693 + x = 0.433439526 Solving 0.2692307693 + x = 0.433439526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + x = 0.433439526 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + x = 0.433439526 + -0.2692307693 x = 0.433439526 + -0.2692307693 Combine like terms: 0.433439526 + -0.2692307693 = 0.1642087567 x = 0.1642087567 Simplifying x = 0.1642087567Subproblem 2
x + 0.2692307693 = -0.433439526 Simplifying x + 0.2692307693 = -0.433439526 Reorder the terms: 0.2692307693 + x = -0.433439526 Solving 0.2692307693 + x = -0.433439526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2692307693' to each side of the equation. 0.2692307693 + -0.2692307693 + x = -0.433439526 + -0.2692307693 Combine like terms: 0.2692307693 + -0.2692307693 = 0.0000000000 0.0000000000 + x = -0.433439526 + -0.2692307693 x = -0.433439526 + -0.2692307693 Combine like terms: -0.433439526 + -0.2692307693 = -0.7026702953 x = -0.7026702953 Simplifying x = -0.7026702953Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1642087567, -0.7026702953}
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