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Simplifying 8x2 + 20x + 3 = 0 Reorder the terms: 3 + 20x + 8x2 = 0 Solving 3 + 20x + 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'. 0.375 + 2.5x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 2.5x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 2.5x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 2.5x + x2 = 0 + -0.375 2.5x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 2.5x + x2 = -0.375 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -0.375 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -0.375 + 1.5625 Combine like terms: -0.375 + 1.5625 = 1.1875 1.5625 + 2.5x + x2 = 1.1875 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 1.1875 Calculate the square root of the right side: 1.089724736 Break this problem into two subproblems by setting (x + 1.25) equal to 1.089724736 and -1.089724736.Subproblem 1
x + 1.25 = 1.089724736 Simplifying x + 1.25 = 1.089724736 Reorder the terms: 1.25 + x = 1.089724736 Solving 1.25 + x = 1.089724736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.089724736 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.089724736 + -1.25 x = 1.089724736 + -1.25 Combine like terms: 1.089724736 + -1.25 = -0.160275264 x = -0.160275264 Simplifying x = -0.160275264Subproblem 2
x + 1.25 = -1.089724736 Simplifying x + 1.25 = -1.089724736 Reorder the terms: 1.25 + x = -1.089724736 Solving 1.25 + x = -1.089724736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.089724736 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.089724736 + -1.25 x = -1.089724736 + -1.25 Combine like terms: -1.089724736 + -1.25 = -2.339724736 x = -2.339724736 Simplifying x = -2.339724736Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.160275264, -2.339724736}
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