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Simplifying 5x2 + 16x + -40 = 0 Reorder the terms: -40 + 16x + 5x2 = 0 Solving -40 + 16x + 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 + 3.2x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 3.2x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 3.2x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3.2x + x2 = 0 + 8 3.2x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 3.2x + x2 = 8 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = 8 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = 8 + 2.56 Combine like terms: 8 + 2.56 = 10.56 2.56 + 3.2x + x2 = 10.56 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 10.56 Calculate the square root of the right side: 3.249615362 Break this problem into two subproblems by setting (x + 1.6) equal to 3.249615362 and -3.249615362.Subproblem 1
x + 1.6 = 3.249615362 Simplifying x + 1.6 = 3.249615362 Reorder the terms: 1.6 + x = 3.249615362 Solving 1.6 + x = 3.249615362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 3.249615362 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 3.249615362 + -1.6 x = 3.249615362 + -1.6 Combine like terms: 3.249615362 + -1.6 = 1.649615362 x = 1.649615362 Simplifying x = 1.649615362Subproblem 2
x + 1.6 = -3.249615362 Simplifying x + 1.6 = -3.249615362 Reorder the terms: 1.6 + x = -3.249615362 Solving 1.6 + x = -3.249615362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -3.249615362 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -3.249615362 + -1.6 x = -3.249615362 + -1.6 Combine like terms: -3.249615362 + -1.6 = -4.849615362 x = -4.849615362 Simplifying x = -4.849615362Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.649615362, -4.849615362}
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