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Simplifying 4x2 + 19x + 19 = 0 Reorder the terms: 19 + 19x + 4x2 = 0 Solving 19 + 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'. 4.75 + 4.75x + x2 = 0 Move the constant term to the right: Add '-4.75' to each side of the equation. 4.75 + 4.75x + -4.75 + x2 = 0 + -4.75 Reorder the terms: 4.75 + -4.75 + 4.75x + x2 = 0 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + 4.75x + x2 = 0 + -4.75 4.75x + x2 = 0 + -4.75 Combine like terms: 0 + -4.75 = -4.75 4.75x + x2 = -4.75 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 = -4.75 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = -4.75 + 5.640625 Combine like terms: -4.75 + 5.640625 = 0.890625 5.640625 + 4.75x + x2 = 0.890625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + 2.375) equal to 0.943729304 and -0.943729304.Subproblem 1
x + 2.375 = 0.943729304 Simplifying x + 2.375 = 0.943729304 Reorder the terms: 2.375 + x = 0.943729304 Solving 2.375 + x = 0.943729304 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 = 0.943729304 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 0.943729304 + -2.375 x = 0.943729304 + -2.375 Combine like terms: 0.943729304 + -2.375 = -1.431270696 x = -1.431270696 Simplifying x = -1.431270696Subproblem 2
x + 2.375 = -0.943729304 Simplifying x + 2.375 = -0.943729304 Reorder the terms: 2.375 + x = -0.943729304 Solving 2.375 + x = -0.943729304 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 = -0.943729304 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -0.943729304 + -2.375 x = -0.943729304 + -2.375 Combine like terms: -0.943729304 + -2.375 = -3.318729304 x = -3.318729304 Simplifying x = -3.318729304Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.431270696, -3.318729304}
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