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Simplifying 8x2 + 69x + 120 = 0 Reorder the terms: 120 + 69x + 8x2 = 0 Solving 120 + 69x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 15 + 8.625x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + 8.625x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 8.625x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 8.625x + x2 = 0 + -15 8.625x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 8.625x + x2 = -15 The x term is 8.625x. Take half its coefficient (4.3125). Square it (18.59765625) and add it to both sides. Add '18.59765625' to each side of the equation. 8.625x + 18.59765625 + x2 = -15 + 18.59765625 Reorder the terms: 18.59765625 + 8.625x + x2 = -15 + 18.59765625 Combine like terms: -15 + 18.59765625 = 3.59765625 18.59765625 + 8.625x + x2 = 3.59765625 Factor a perfect square on the left side: (x + 4.3125)(x + 4.3125) = 3.59765625 Calculate the square root of the right side: 1.896748863 Break this problem into two subproblems by setting (x + 4.3125) equal to 1.896748863 and -1.896748863.Subproblem 1
x + 4.3125 = 1.896748863 Simplifying x + 4.3125 = 1.896748863 Reorder the terms: 4.3125 + x = 1.896748863 Solving 4.3125 + x = 1.896748863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.3125' to each side of the equation. 4.3125 + -4.3125 + x = 1.896748863 + -4.3125 Combine like terms: 4.3125 + -4.3125 = 0.0000 0.0000 + x = 1.896748863 + -4.3125 x = 1.896748863 + -4.3125 Combine like terms: 1.896748863 + -4.3125 = -2.415751137 x = -2.415751137 Simplifying x = -2.415751137Subproblem 2
x + 4.3125 = -1.896748863 Simplifying x + 4.3125 = -1.896748863 Reorder the terms: 4.3125 + x = -1.896748863 Solving 4.3125 + x = -1.896748863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.3125' to each side of the equation. 4.3125 + -4.3125 + x = -1.896748863 + -4.3125 Combine like terms: 4.3125 + -4.3125 = 0.0000 0.0000 + x = -1.896748863 + -4.3125 x = -1.896748863 + -4.3125 Combine like terms: -1.896748863 + -4.3125 = -6.209248863 x = -6.209248863 Simplifying x = -6.209248863Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.415751137, -6.209248863}
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