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Simplifying 2.5x2 + 3x + 0.5 = 0 Reorder the terms: 0.5 + 3x + 2.5x2 = 0 Solving 0.5 + 3x + 2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 0.2 + 1.2x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 1.2x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 1.2x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 1.2x + x2 = 0 + -0.2 1.2x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 1.2x + x2 = -0.2 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = -0.2 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = -0.2 + 0.36 Combine like terms: -0.2 + 0.36 = 0.16 0.36 + 1.2x + x2 = 0.16 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.16 Calculate the square root of the right side: 0.4 Break this problem into two subproblems by setting (x + 0.6) equal to 0.4 and -0.4.Subproblem 1
x + 0.6 = 0.4 Simplifying x + 0.6 = 0.4 Reorder the terms: 0.6 + x = 0.4 Solving 0.6 + x = 0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 0.4 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.4 + -0.6 x = 0.4 + -0.6 Combine like terms: 0.4 + -0.6 = -0.2 x = -0.2 Simplifying x = -0.2Subproblem 2
x + 0.6 = -0.4 Simplifying x + 0.6 = -0.4 Reorder the terms: 0.6 + x = -0.4 Solving 0.6 + x = -0.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -0.4 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.4 + -0.6 x = -0.4 + -0.6 Combine like terms: -0.4 + -0.6 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2, -1}
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