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Simplifying 0.2x2 + -5x + -90 = 0 Reorder the terms: -90 + -5x + 0.2x2 = 0 Solving -90 + -5x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -450 + -25x + x2 = 0 Move the constant term to the right: Add '450' to each side of the equation. -450 + -25x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + -25x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + -25x + x2 = 0 + 450 -25x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 -25x + x2 = 450 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = 450 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 450 + 156.25 Combine like terms: 450 + 156.25 = 606.25 156.25 + -25x + x2 = 606.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 606.25 Calculate the square root of the right side: 24.622144504 Break this problem into two subproblems by setting (x + -12.5) equal to 24.622144504 and -24.622144504.Subproblem 1
x + -12.5 = 24.622144504 Simplifying x + -12.5 = 24.622144504 Reorder the terms: -12.5 + x = 24.622144504 Solving -12.5 + x = 24.622144504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 24.622144504 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 24.622144504 + 12.5 x = 24.622144504 + 12.5 Combine like terms: 24.622144504 + 12.5 = 37.122144504 x = 37.122144504 Simplifying x = 37.122144504Subproblem 2
x + -12.5 = -24.622144504 Simplifying x + -12.5 = -24.622144504 Reorder the terms: -12.5 + x = -24.622144504 Solving -12.5 + x = -24.622144504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -24.622144504 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -24.622144504 + 12.5 x = -24.622144504 + 12.5 Combine like terms: -24.622144504 + 12.5 = -12.122144504 x = -12.122144504 Simplifying x = -12.122144504Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.122144504, -12.122144504}
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