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Simplifying 4x2 + 19x + 16 = 0 Reorder the terms: 16 + 19x + 4x2 = 0 Solving 16 + 19x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4 + 4.75x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 4.75x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 4.75x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 4.75x + x2 = 0 + -4 4.75x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 4.75x + x2 = -4 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = -4 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = -4 + 5.640625 Combine like terms: -4 + 5.640625 = 1.640625 5.640625 + 4.75x + x2 = 1.640625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + 2.375) equal to 1.280868846 and -1.280868846.Subproblem 1
x + 2.375 = 1.280868846 Simplifying x + 2.375 = 1.280868846 Reorder the terms: 2.375 + x = 1.280868846 Solving 2.375 + x = 1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 1.280868846 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 1.280868846 + -2.375 x = 1.280868846 + -2.375 Combine like terms: 1.280868846 + -2.375 = -1.094131154 x = -1.094131154 Simplifying x = -1.094131154Subproblem 2
x + 2.375 = -1.280868846 Simplifying x + 2.375 = -1.280868846 Reorder the terms: 2.375 + x = -1.280868846 Solving 2.375 + x = -1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -1.280868846 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -1.280868846 + -2.375 x = -1.280868846 + -2.375 Combine like terms: -1.280868846 + -2.375 = -3.655868846 x = -3.655868846 Simplifying x = -3.655868846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.094131154, -3.655868846}
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