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Simplifying 5x2 + 4x + -40 = 0 Reorder the terms: -40 + 4x + 5x2 = 0 Solving -40 + 4x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8 + 0.8x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 0.8x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 0.8x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 0.8x + x2 = 0 + 8 0.8x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 0.8x + x2 = 8 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 8 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 8 + 0.16 Combine like terms: 8 + 0.16 = 8.16 0.16 + 0.8x + x2 = 8.16 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 8.16 Calculate the square root of the right side: 2.856571371 Break this problem into two subproblems by setting (x + 0.4) equal to 2.856571371 and -2.856571371.Subproblem 1
x + 0.4 = 2.856571371 Simplifying x + 0.4 = 2.856571371 Reorder the terms: 0.4 + x = 2.856571371 Solving 0.4 + x = 2.856571371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 2.856571371 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 2.856571371 + -0.4 x = 2.856571371 + -0.4 Combine like terms: 2.856571371 + -0.4 = 2.456571371 x = 2.456571371 Simplifying x = 2.456571371Subproblem 2
x + 0.4 = -2.856571371 Simplifying x + 0.4 = -2.856571371 Reorder the terms: 0.4 + x = -2.856571371 Solving 0.4 + x = -2.856571371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -2.856571371 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -2.856571371 + -0.4 x = -2.856571371 + -0.4 Combine like terms: -2.856571371 + -0.4 = -3.256571371 x = -3.256571371 Simplifying x = -3.256571371Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.456571371, -3.256571371}
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