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Simplifying 0.64x2 + 2.72x + 0.64 = 0 Reorder the terms: 0.64 + 2.72x + 0.64x2 = 0 Solving 0.64 + 2.72x + 0.64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.64 the coefficient of the squared term: Divide each side by '0.64'. 1 + 4.25x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4.25x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 4.25x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4.25x + x2 = 0 + -1 4.25x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 4.25x + x2 = -1 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = -1 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = -1 + 4.515625 Combine like terms: -1 + 4.515625 = 3.515625 4.515625 + 4.25x + x2 = 3.515625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 3.515625 Calculate the square root of the right side: 1.875 Break this problem into two subproblems by setting (x + 2.125) equal to 1.875 and -1.875.Subproblem 1
x + 2.125 = 1.875 Simplifying x + 2.125 = 1.875 Reorder the terms: 2.125 + x = 1.875 Solving 2.125 + x = 1.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 1.875 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 1.875 + -2.125 x = 1.875 + -2.125 Combine like terms: 1.875 + -2.125 = -0.25 x = -0.25 Simplifying x = -0.25Subproblem 2
x + 2.125 = -1.875 Simplifying x + 2.125 = -1.875 Reorder the terms: 2.125 + x = -1.875 Solving 2.125 + x = -1.875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -1.875 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -1.875 + -2.125 x = -1.875 + -2.125 Combine like terms: -1.875 + -2.125 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.25, -4}
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