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Simplifying 2.5x2 + 4x + -40 = 0 Reorder the terms: -40 + 4x + 2.5x2 = 0 Solving -40 + 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'. -16 + 1.6x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 1.6x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 1.6x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 1.6x + x2 = 0 + 16 1.6x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 1.6x + x2 = 16 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 = 16 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 16 + 0.64 Combine like terms: 16 + 0.64 = 16.64 0.64 + 1.6x + x2 = 16.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 16.64 Calculate the square root of the right side: 4.079215611 Break this problem into two subproblems by setting (x + 0.8) equal to 4.079215611 and -4.079215611.Subproblem 1
x + 0.8 = 4.079215611 Simplifying x + 0.8 = 4.079215611 Reorder the terms: 0.8 + x = 4.079215611 Solving 0.8 + x = 4.079215611 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 = 4.079215611 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 4.079215611 + -0.8 x = 4.079215611 + -0.8 Combine like terms: 4.079215611 + -0.8 = 3.279215611 x = 3.279215611 Simplifying x = 3.279215611Subproblem 2
x + 0.8 = -4.079215611 Simplifying x + 0.8 = -4.079215611 Reorder the terms: 0.8 + x = -4.079215611 Solving 0.8 + x = -4.079215611 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 = -4.079215611 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -4.079215611 + -0.8 x = -4.079215611 + -0.8 Combine like terms: -4.079215611 + -0.8 = -4.879215611 x = -4.879215611 Simplifying x = -4.879215611Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.279215611, -4.879215611}
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