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Simplifying -1x2 + 10x + 30000 = 0 Reorder the terms: 30000 + 10x + -1x2 = 0 Solving 30000 + 10x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30000 + -10x + x2 = 0 Move the constant term to the right: Add '30000' to each side of the equation. -30000 + -10x + 30000 + x2 = 0 + 30000 Reorder the terms: -30000 + 30000 + -10x + x2 = 0 + 30000 Combine like terms: -30000 + 30000 = 0 0 + -10x + x2 = 0 + 30000 -10x + x2 = 0 + 30000 Combine like terms: 0 + 30000 = 30000 -10x + x2 = 30000 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 30000 + 25 Reorder the terms: 25 + -10x + x2 = 30000 + 25 Combine like terms: 30000 + 25 = 30025 25 + -10x + x2 = 30025 Factor a perfect square on the left side: (x + -5)(x + -5) = 30025 Calculate the square root of the right side: 173.277234512 Break this problem into two subproblems by setting (x + -5) equal to 173.277234512 and -173.277234512.Subproblem 1
x + -5 = 173.277234512 Simplifying x + -5 = 173.277234512 Reorder the terms: -5 + x = 173.277234512 Solving -5 + x = 173.277234512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 173.277234512 + 5 Combine like terms: -5 + 5 = 0 0 + x = 173.277234512 + 5 x = 173.277234512 + 5 Combine like terms: 173.277234512 + 5 = 178.277234512 x = 178.277234512 Simplifying x = 178.277234512Subproblem 2
x + -5 = -173.277234512 Simplifying x + -5 = -173.277234512 Reorder the terms: -5 + x = -173.277234512 Solving -5 + x = -173.277234512 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -173.277234512 + 5 Combine like terms: -5 + 5 = 0 0 + x = -173.277234512 + 5 x = -173.277234512 + 5 Combine like terms: -173.277234512 + 5 = -168.277234512 x = -168.277234512 Simplifying x = -168.277234512Solution
The solution to the problem is based on the solutions from the subproblems. x = {178.277234512, -168.277234512}
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