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Simplifying 2.5x2 + -1x + -0.8 = 0 Reorder the terms: -0.8 + -1x + 2.5x2 = 0 Solving -0.8 + -1x + 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'. -0.32 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.32' to each side of the equation. -0.32 + -0.4x + 0.32 + x2 = 0 + 0.32 Reorder the terms: -0.32 + 0.32 + -0.4x + x2 = 0 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + -0.4x + x2 = 0 + 0.32 -0.4x + x2 = 0 + 0.32 Combine like terms: 0 + 0.32 = 0.32 -0.4x + x2 = 0.32 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 = 0.32 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.32 + 0.04 Combine like terms: 0.32 + 0.04 = 0.36 0.04 + -0.4x + x2 = 0.36 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.36 Calculate the square root of the right side: 0.6 Break this problem into two subproblems by setting (x + -0.2) equal to 0.6 and -0.6.Subproblem 1
x + -0.2 = 0.6 Simplifying x + -0.2 = 0.6 Reorder the terms: -0.2 + x = 0.6 Solving -0.2 + x = 0.6 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 = 0.6 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.6 + 0.2 x = 0.6 + 0.2 Combine like terms: 0.6 + 0.2 = 0.8 x = 0.8 Simplifying x = 0.8Subproblem 2
x + -0.2 = -0.6 Simplifying x + -0.2 = -0.6 Reorder the terms: -0.2 + x = -0.6 Solving -0.2 + x = -0.6 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 = -0.6 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.6 + 0.2 x = -0.6 + 0.2 Combine like terms: -0.6 + 0.2 = -0.4 x = -0.4 Simplifying x = -0.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8, -0.4}
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