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Simplifying 5x2 + -14x + -44 = 0 Reorder the terms: -44 + -14x + 5x2 = 0 Solving -44 + -14x + 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'. -8.8 + -2.8x + x2 = 0 Move the constant term to the right: Add '8.8' to each side of the equation. -8.8 + -2.8x + 8.8 + x2 = 0 + 8.8 Reorder the terms: -8.8 + 8.8 + -2.8x + x2 = 0 + 8.8 Combine like terms: -8.8 + 8.8 = 0.0 0.0 + -2.8x + x2 = 0 + 8.8 -2.8x + x2 = 0 + 8.8 Combine like terms: 0 + 8.8 = 8.8 -2.8x + x2 = 8.8 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = 8.8 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = 8.8 + 1.96 Combine like terms: 8.8 + 1.96 = 10.76 1.96 + -2.8x + x2 = 10.76 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 10.76 Calculate the square root of the right side: 3.280243893 Break this problem into two subproblems by setting (x + -1.4) equal to 3.280243893 and -3.280243893.Subproblem 1
x + -1.4 = 3.280243893 Simplifying x + -1.4 = 3.280243893 Reorder the terms: -1.4 + x = 3.280243893 Solving -1.4 + x = 3.280243893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 3.280243893 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 3.280243893 + 1.4 x = 3.280243893 + 1.4 Combine like terms: 3.280243893 + 1.4 = 4.680243893 x = 4.680243893 Simplifying x = 4.680243893Subproblem 2
x + -1.4 = -3.280243893 Simplifying x + -1.4 = -3.280243893 Reorder the terms: -1.4 + x = -3.280243893 Solving -1.4 + x = -3.280243893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -3.280243893 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -3.280243893 + 1.4 x = -3.280243893 + 1.4 Combine like terms: -3.280243893 + 1.4 = -1.880243893 x = -1.880243893 Simplifying x = -1.880243893Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.680243893, -1.880243893}
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