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Simplifying x + (x * x * 0.2) = 420 Reorder the terms for easier multiplication: x + (0.2x * x) = 420 Multiply x * x x + (0.2x2) = 420 Solving x + (0.2x2) = 420 Solving for variable 'x'. Reorder the terms: -420 + x + (0.2x2) = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + x + (0.2x2) = 0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -2100 + 5x + x2 = 0 Move the constant term to the right: Add '2100' to each side of the equation. -2100 + 5x + 2100 + x2 = 0 + 2100 Reorder the terms: -2100 + 2100 + 5x + x2 = 0 + 2100 Combine like terms: -2100 + 2100 = 0 0 + 5x + x2 = 0 + 2100 5x + x2 = 0 + 2100 Combine like terms: 0 + 2100 = 2100 5x + x2 = 2100 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 5x + 0.25 + x2 = 2100 + 0.25 Reorder the terms: 0.25 + 5x + x2 = 2100 + 0.25 Combine like terms: 2100 + 0.25 = 2100.25 0.25 + 5x + x2 = 2100.25 Factor a perfect square on the left side: ((x) + 0.5)((x) + 0.5) = 2100.25 Calculate the square root of the right side: 45.828484592 Break this problem into two subproblems by setting ((x) + 0.5) equal to 45.828484592 and -45.828484592.Subproblem 1
(x) + 0.5 = 45.828484592 Simplifying (x) + 0.5 = 45.828484592 x + 0.5 = 45.828484592 Reorder the terms: 0.5 + x = 45.828484592 Solving 0.5 + x = 45.828484592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 45.828484592 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 45.828484592 + -0.5 x = 45.828484592 + -0.5 Combine like terms: 45.828484592 + -0.5 = 45.328484592 x = 45.328484592 Simplifying x = 45.328484592Subproblem 2
(x) + 0.5 = -45.828484592 Simplifying (x) + 0.5 = -45.828484592 x + 0.5 = -45.828484592 Reorder the terms: 0.5 + x = -45.828484592 Solving 0.5 + x = -45.828484592 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -45.828484592 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -45.828484592 + -0.5 x = -45.828484592 + -0.5 Combine like terms: -45.828484592 + -0.5 = -46.328484592 x = -46.328484592 Simplifying x = -46.328484592Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.328484592, -46.328484592}
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