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Simplifying 0.2x2 + 7x + 150 = 210 Reorder the terms: 150 + 7x + 0.2x2 = 210 Solving 150 + 7x + 0.2x2 = 210 Solving for variable 'x'. Reorder the terms: 150 + -210 + 7x + 0.2x2 = 210 + -210 Combine like terms: 150 + -210 = -60 -60 + 7x + 0.2x2 = 210 + -210 Combine like terms: 210 + -210 = 0 -60 + 7x + 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'. -300 + 35x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + 35x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 35x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 35x + x2 = 0 + 300 35x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 35x + x2 = 300 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = 300 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 300 + 306.25 Combine like terms: 300 + 306.25 = 606.25 306.25 + 35x + x2 = 606.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 606.25 Calculate the square root of the right side: 24.622144504 Break this problem into two subproblems by setting (x + 17.5) equal to 24.622144504 and -24.622144504.Subproblem 1
x + 17.5 = 24.622144504 Simplifying x + 17.5 = 24.622144504 Reorder the terms: 17.5 + x = 24.622144504 Solving 17.5 + x = 24.622144504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 24.622144504 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 24.622144504 + -17.5 x = 24.622144504 + -17.5 Combine like terms: 24.622144504 + -17.5 = 7.122144504 x = 7.122144504 Simplifying x = 7.122144504Subproblem 2
x + 17.5 = -24.622144504 Simplifying x + 17.5 = -24.622144504 Reorder the terms: 17.5 + x = -24.622144504 Solving 17.5 + x = -24.622144504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -24.622144504 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -24.622144504 + -17.5 x = -24.622144504 + -17.5 Combine like terms: -24.622144504 + -17.5 = -42.122144504 x = -42.122144504 Simplifying x = -42.122144504Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.122144504, -42.122144504}
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