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Simplifying 5x2 + 8x + -2020 = 0 Reorder the terms: -2020 + 8x + 5x2 = 0 Solving -2020 + 8x + 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'. -404 + 1.6x + x2 = 0 Move the constant term to the right: Add '404' to each side of the equation. -404 + 1.6x + 404 + x2 = 0 + 404 Reorder the terms: -404 + 404 + 1.6x + x2 = 0 + 404 Combine like terms: -404 + 404 = 0 0 + 1.6x + x2 = 0 + 404 1.6x + x2 = 0 + 404 Combine like terms: 0 + 404 = 404 1.6x + x2 = 404 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 = 404 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 404 + 0.64 Combine like terms: 404 + 0.64 = 404.64 0.64 + 1.6x + x2 = 404.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 404.64 Calculate the square root of the right side: 20.115665537 Break this problem into two subproblems by setting (x + 0.8) equal to 20.115665537 and -20.115665537.Subproblem 1
x + 0.8 = 20.115665537 Simplifying x + 0.8 = 20.115665537 Reorder the terms: 0.8 + x = 20.115665537 Solving 0.8 + x = 20.115665537 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 = 20.115665537 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 20.115665537 + -0.8 x = 20.115665537 + -0.8 Combine like terms: 20.115665537 + -0.8 = 19.315665537 x = 19.315665537 Simplifying x = 19.315665537Subproblem 2
x + 0.8 = -20.115665537 Simplifying x + 0.8 = -20.115665537 Reorder the terms: 0.8 + x = -20.115665537 Solving 0.8 + x = -20.115665537 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 = -20.115665537 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -20.115665537 + -0.8 x = -20.115665537 + -0.8 Combine like terms: -20.115665537 + -0.8 = -20.915665537 x = -20.915665537 Simplifying x = -20.915665537Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.315665537, -20.915665537}
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