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Simplifying 5x2 + 44x + 94 = 0 Reorder the terms: 94 + 44x + 5x2 = 0 Solving 94 + 44x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 18.8 + 8.8x + x2 = 0 Move the constant term to the right: Add '-18.8' to each side of the equation. 18.8 + 8.8x + -18.8 + x2 = 0 + -18.8 Reorder the terms: 18.8 + -18.8 + 8.8x + x2 = 0 + -18.8 Combine like terms: 18.8 + -18.8 = 0.0 0.0 + 8.8x + x2 = 0 + -18.8 8.8x + x2 = 0 + -18.8 Combine like terms: 0 + -18.8 = -18.8 8.8x + x2 = -18.8 The x term is 8.8x. Take half its coefficient (4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. 8.8x + 19.36 + x2 = -18.8 + 19.36 Reorder the terms: 19.36 + 8.8x + x2 = -18.8 + 19.36 Combine like terms: -18.8 + 19.36 = 0.56 19.36 + 8.8x + x2 = 0.56 Factor a perfect square on the left side: (x + 4.4)(x + 4.4) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (x + 4.4) equal to 0.748331477 and -0.748331477.Subproblem 1
x + 4.4 = 0.748331477 Simplifying x + 4.4 = 0.748331477 Reorder the terms: 4.4 + x = 0.748331477 Solving 4.4 + x = 0.748331477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = 0.748331477 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = 0.748331477 + -4.4 x = 0.748331477 + -4.4 Combine like terms: 0.748331477 + -4.4 = -3.651668523 x = -3.651668523 Simplifying x = -3.651668523Subproblem 2
x + 4.4 = -0.748331477 Simplifying x + 4.4 = -0.748331477 Reorder the terms: 4.4 + x = -0.748331477 Solving 4.4 + x = -0.748331477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = -0.748331477 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = -0.748331477 + -4.4 x = -0.748331477 + -4.4 Combine like terms: -0.748331477 + -4.4 = -5.148331477 x = -5.148331477 Simplifying x = -5.148331477Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.651668523, -5.148331477}
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