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Simplifying 0 = -5x2 + -28x + 9 Reorder the terms: 0 = 9 + -28x + -5x2 Solving 0 = 9 + -28x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + 28x + 5x2 = 9 + -28x + -5x2 + -9 + 28x + 5x2 Reorder the terms: -9 + 28x + 5x2 = 9 + -9 + -28x + 28x + -5x2 + 5x2 Combine like terms: 9 + -9 = 0 -9 + 28x + 5x2 = 0 + -28x + 28x + -5x2 + 5x2 -9 + 28x + 5x2 = -28x + 28x + -5x2 + 5x2 Combine like terms: -28x + 28x = 0 -9 + 28x + 5x2 = 0 + -5x2 + 5x2 -9 + 28x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -9 + 28x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 5.6x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 5.6x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 5.6x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 5.6x + x2 = 0 + 1.8 5.6x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 5.6x + x2 = 1.8 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 = 1.8 + 7.84 Reorder the terms: 7.84 + 5.6x + x2 = 1.8 + 7.84 Combine like terms: 1.8 + 7.84 = 9.64 7.84 + 5.6x + x2 = 9.64 Factor a perfect square on the left side: (x + 2.8)(x + 2.8) = 9.64 Calculate the square root of the right side: 3.104834939 Break this problem into two subproblems by setting (x + 2.8) equal to 3.104834939 and -3.104834939.Subproblem 1
x + 2.8 = 3.104834939 Simplifying x + 2.8 = 3.104834939 Reorder the terms: 2.8 + x = 3.104834939 Solving 2.8 + x = 3.104834939 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 = 3.104834939 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = 3.104834939 + -2.8 x = 3.104834939 + -2.8 Combine like terms: 3.104834939 + -2.8 = 0.304834939 x = 0.304834939 Simplifying x = 0.304834939Subproblem 2
x + 2.8 = -3.104834939 Simplifying x + 2.8 = -3.104834939 Reorder the terms: 2.8 + x = -3.104834939 Solving 2.8 + x = -3.104834939 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 = -3.104834939 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = -3.104834939 + -2.8 x = -3.104834939 + -2.8 Combine like terms: -3.104834939 + -2.8 = -5.904834939 x = -5.904834939 Simplifying x = -5.904834939Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.304834939, -5.904834939}
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