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Simplifying -0.39 + 2.5x + 6.25x2 = 0 Solving -0.39 + 2.5x + 6.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.25 the coefficient of the squared term: Divide each side by '6.25'. -0.0624 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.0624' to each side of the equation. -0.0624 + 0.4x + 0.0624 + x2 = 0 + 0.0624 Reorder the terms: -0.0624 + 0.0624 + 0.4x + x2 = 0 + 0.0624 Combine like terms: -0.0624 + 0.0624 = 0.0000 0.0000 + 0.4x + x2 = 0 + 0.0624 0.4x + x2 = 0 + 0.0624 Combine like terms: 0 + 0.0624 = 0.0624 0.4x + x2 = 0.0624 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.0624 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.0624 + 0.04 Combine like terms: 0.0624 + 0.04 = 0.1024 0.04 + 0.4x + x2 = 0.1024 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.1024 Calculate the square root of the right side: 0.32 Break this problem into two subproblems by setting (x + 0.2) equal to 0.32 and -0.32.Subproblem 1
x + 0.2 = 0.32 Simplifying x + 0.2 = 0.32 Reorder the terms: 0.2 + x = 0.32 Solving 0.2 + x = 0.32 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.32 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.32 + -0.2 x = 0.32 + -0.2 Combine like terms: 0.32 + -0.2 = 0.12 x = 0.12 Simplifying x = 0.12Subproblem 2
x + 0.2 = -0.32 Simplifying x + 0.2 = -0.32 Reorder the terms: 0.2 + x = -0.32 Solving 0.2 + x = -0.32 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.32 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.32 + -0.2 x = -0.32 + -0.2 Combine like terms: -0.32 + -0.2 = -0.52 x = -0.52 Simplifying x = -0.52Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.12, -0.52}
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