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Simplifying 5x2 + 28x + -28 = 0 Reorder the terms: -28 + 28x + 5x2 = 0 Solving -28 + 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'. -5.6 + 5.6x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 5.6x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 5.6x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 5.6x + x2 = 0 + 5.6 5.6x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 5.6x + x2 = 5.6 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 = 5.6 + 7.84 Reorder the terms: 7.84 + 5.6x + x2 = 5.6 + 7.84 Combine like terms: 5.6 + 7.84 = 13.44 7.84 + 5.6x + x2 = 13.44 Factor a perfect square on the left side: (x + 2.8)(x + 2.8) = 13.44 Calculate the square root of the right side: 3.666060556 Break this problem into two subproblems by setting (x + 2.8) equal to 3.666060556 and -3.666060556.Subproblem 1
x + 2.8 = 3.666060556 Simplifying x + 2.8 = 3.666060556 Reorder the terms: 2.8 + x = 3.666060556 Solving 2.8 + x = 3.666060556 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 = 3.666060556 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = 3.666060556 + -2.8 x = 3.666060556 + -2.8 Combine like terms: 3.666060556 + -2.8 = 0.866060556 x = 0.866060556 Simplifying x = 0.866060556Subproblem 2
x + 2.8 = -3.666060556 Simplifying x + 2.8 = -3.666060556 Reorder the terms: 2.8 + x = -3.666060556 Solving 2.8 + x = -3.666060556 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 = -3.666060556 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = -3.666060556 + -2.8 x = -3.666060556 + -2.8 Combine like terms: -3.666060556 + -2.8 = -6.466060556 x = -6.466060556 Simplifying x = -6.466060556Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.866060556, -6.466060556}
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