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Simplifying 5x2 + -28x + -4 = 0 Reorder the terms: -4 + -28x + 5x2 = 0 Solving -4 + -28x + 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'. -0.8 + -5.6x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -5.6x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -5.6x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -5.6x + x2 = 0 + 0.8 -5.6x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -5.6x + x2 = 0.8 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = 0.8 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = 0.8 + 7.84 Combine like terms: 0.8 + 7.84 = 8.64 7.84 + -5.6x + x2 = 8.64 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 8.64 Calculate the square root of the right side: 2.939387691 Break this problem into two subproblems by setting (x + -2.8) equal to 2.939387691 and -2.939387691.Subproblem 1
x + -2.8 = 2.939387691 Simplifying x + -2.8 = 2.939387691 Reorder the terms: -2.8 + x = 2.939387691 Solving -2.8 + x = 2.939387691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 2.939387691 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 2.939387691 + 2.8 x = 2.939387691 + 2.8 Combine like terms: 2.939387691 + 2.8 = 5.739387691 x = 5.739387691 Simplifying x = 5.739387691Subproblem 2
x + -2.8 = -2.939387691 Simplifying x + -2.8 = -2.939387691 Reorder the terms: -2.8 + x = -2.939387691 Solving -2.8 + x = -2.939387691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -2.939387691 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -2.939387691 + 2.8 x = -2.939387691 + 2.8 Combine like terms: -2.939387691 + 2.8 = -0.139387691 x = -0.139387691 Simplifying x = -0.139387691Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.739387691, -0.139387691}
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