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Simplifying 14x2 = 19x + 5 Reorder the terms: 14x2 = 5 + 19x Solving 14x2 = 5 + 19x Solving for variable 'x'. Reorder the terms: -5 + -19x + 14x2 = 5 + 19x + -5 + -19x Reorder the terms: -5 + -19x + 14x2 = 5 + -5 + 19x + -19x Combine like terms: 5 + -5 = 0 -5 + -19x + 14x2 = 0 + 19x + -19x -5 + -19x + 14x2 = 19x + -19x Combine like terms: 19x + -19x = 0 -5 + -19x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.3571428571 + -1.357142857x + x2 = 0 Move the constant term to the right: Add '0.3571428571' to each side of the equation. -0.3571428571 + -1.357142857x + 0.3571428571 + x2 = 0 + 0.3571428571 Reorder the terms: -0.3571428571 + 0.3571428571 + -1.357142857x + x2 = 0 + 0.3571428571 Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000 0.0000000000 + -1.357142857x + x2 = 0 + 0.3571428571 -1.357142857x + x2 = 0 + 0.3571428571 Combine like terms: 0 + 0.3571428571 = 0.3571428571 -1.357142857x + x2 = 0.3571428571 The x term is -1.357142857x. Take half its coefficient (-0.6785714285). Square it (0.4604591836) and add it to both sides. Add '0.4604591836' to each side of the equation. -1.357142857x + 0.4604591836 + x2 = 0.3571428571 + 0.4604591836 Reorder the terms: 0.4604591836 + -1.357142857x + x2 = 0.3571428571 + 0.4604591836 Combine like terms: 0.3571428571 + 0.4604591836 = 0.8176020407 0.4604591836 + -1.357142857x + x2 = 0.8176020407 Factor a perfect square on the left side: (x + -0.6785714285)(x + -0.6785714285) = 0.8176020407 Calculate the square root of the right side: 0.904213493 Break this problem into two subproblems by setting (x + -0.6785714285) equal to 0.904213493 and -0.904213493.Subproblem 1
x + -0.6785714285 = 0.904213493 Simplifying x + -0.6785714285 = 0.904213493 Reorder the terms: -0.6785714285 + x = 0.904213493 Solving -0.6785714285 + x = 0.904213493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6785714285' to each side of the equation. -0.6785714285 + 0.6785714285 + x = 0.904213493 + 0.6785714285 Combine like terms: -0.6785714285 + 0.6785714285 = 0.0000000000 0.0000000000 + x = 0.904213493 + 0.6785714285 x = 0.904213493 + 0.6785714285 Combine like terms: 0.904213493 + 0.6785714285 = 1.5827849215 x = 1.5827849215 Simplifying x = 1.5827849215Subproblem 2
x + -0.6785714285 = -0.904213493 Simplifying x + -0.6785714285 = -0.904213493 Reorder the terms: -0.6785714285 + x = -0.904213493 Solving -0.6785714285 + x = -0.904213493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6785714285' to each side of the equation. -0.6785714285 + 0.6785714285 + x = -0.904213493 + 0.6785714285 Combine like terms: -0.6785714285 + 0.6785714285 = 0.0000000000 0.0000000000 + x = -0.904213493 + 0.6785714285 x = -0.904213493 + 0.6785714285 Combine like terms: -0.904213493 + 0.6785714285 = -0.2256420645 x = -0.2256420645 Simplifying x = -0.2256420645Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5827849215, -0.2256420645}
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