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Simplifying 2.5x2 + 4x + -128 = 0 Reorder the terms: -128 + 4x + 2.5x2 = 0 Solving -128 + 4x + 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'. -51.2 + 1.6x + x2 = 0 Move the constant term to the right: Add '51.2' to each side of the equation. -51.2 + 1.6x + 51.2 + x2 = 0 + 51.2 Reorder the terms: -51.2 + 51.2 + 1.6x + x2 = 0 + 51.2 Combine like terms: -51.2 + 51.2 = 0.0 0.0 + 1.6x + x2 = 0 + 51.2 1.6x + x2 = 0 + 51.2 Combine like terms: 0 + 51.2 = 51.2 1.6x + x2 = 51.2 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 51.2 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 51.2 + 0.64 Combine like terms: 51.2 + 0.64 = 51.84 0.64 + 1.6x + x2 = 51.84 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 51.84 Calculate the square root of the right side: 7.2 Break this problem into two subproblems by setting (x + 0.8) equal to 7.2 and -7.2.Subproblem 1
x + 0.8 = 7.2 Simplifying x + 0.8 = 7.2 Reorder the terms: 0.8 + x = 7.2 Solving 0.8 + x = 7.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 7.2 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 7.2 + -0.8 x = 7.2 + -0.8 Combine like terms: 7.2 + -0.8 = 6.4 x = 6.4 Simplifying x = 6.4Subproblem 2
x + 0.8 = -7.2 Simplifying x + 0.8 = -7.2 Reorder the terms: 0.8 + x = -7.2 Solving 0.8 + x = -7.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -7.2 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -7.2 + -0.8 x = -7.2 + -0.8 Combine like terms: -7.2 + -0.8 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.4, -8}
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