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Simplifying 27200 = x2 + 90x + 200 Reorder the terms: 27200 = 200 + 90x + x2 Solving 27200 = 200 + 90x + x2 Solving for variable 'x'. Combine like terms: 27200 + -200 = 27000 27000 + -90x + -1x2 = 200 + 90x + x2 + -200 + -90x + -1x2 Reorder the terms: 27000 + -90x + -1x2 = 200 + -200 + 90x + -90x + x2 + -1x2 Combine like terms: 200 + -200 = 0 27000 + -90x + -1x2 = 0 + 90x + -90x + x2 + -1x2 27000 + -90x + -1x2 = 90x + -90x + x2 + -1x2 Combine like terms: 90x + -90x = 0 27000 + -90x + -1x2 = 0 + x2 + -1x2 27000 + -90x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 27000 + -90x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -27000 + 90x + x2 = 0 Move the constant term to the right: Add '27000' to each side of the equation. -27000 + 90x + 27000 + x2 = 0 + 27000 Reorder the terms: -27000 + 27000 + 90x + x2 = 0 + 27000 Combine like terms: -27000 + 27000 = 0 0 + 90x + x2 = 0 + 27000 90x + x2 = 0 + 27000 Combine like terms: 0 + 27000 = 27000 90x + x2 = 27000 The x term is 90x. Take half its coefficient (45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. 90x + 2025 + x2 = 27000 + 2025 Reorder the terms: 2025 + 90x + x2 = 27000 + 2025 Combine like terms: 27000 + 2025 = 29025 2025 + 90x + x2 = 29025 Factor a perfect square on the left side: (x + 45)(x + 45) = 29025 Calculate the square root of the right side: 170.367250374 Break this problem into two subproblems by setting (x + 45) equal to 170.367250374 and -170.367250374.Subproblem 1
x + 45 = 170.367250374 Simplifying x + 45 = 170.367250374 Reorder the terms: 45 + x = 170.367250374 Solving 45 + x = 170.367250374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = 170.367250374 + -45 Combine like terms: 45 + -45 = 0 0 + x = 170.367250374 + -45 x = 170.367250374 + -45 Combine like terms: 170.367250374 + -45 = 125.367250374 x = 125.367250374 Simplifying x = 125.367250374Subproblem 2
x + 45 = -170.367250374 Simplifying x + 45 = -170.367250374 Reorder the terms: 45 + x = -170.367250374 Solving 45 + x = -170.367250374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = -170.367250374 + -45 Combine like terms: 45 + -45 = 0 0 + x = -170.367250374 + -45 x = -170.367250374 + -45 Combine like terms: -170.367250374 + -45 = -215.367250374 x = -215.367250374 Simplifying x = -215.367250374Solution
The solution to the problem is based on the solutions from the subproblems. x = {125.367250374, -215.367250374}
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