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Simplifying x2 + 90x + -1200 = 0 Reorder the terms: -1200 + 90x + x2 = 0 Solving -1200 + 90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 90x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 90x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 90x + x2 = 0 + 1200 90x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 90x + x2 = 1200 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 = 1200 + 2025 Reorder the terms: 2025 + 90x + x2 = 1200 + 2025 Combine like terms: 1200 + 2025 = 3225 2025 + 90x + x2 = 3225 Factor a perfect square on the left side: (x + 45)(x + 45) = 3225 Calculate the square root of the right side: 56.789083458 Break this problem into two subproblems by setting (x + 45) equal to 56.789083458 and -56.789083458.Subproblem 1
x + 45 = 56.789083458 Simplifying x + 45 = 56.789083458 Reorder the terms: 45 + x = 56.789083458 Solving 45 + x = 56.789083458 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 = 56.789083458 + -45 Combine like terms: 45 + -45 = 0 0 + x = 56.789083458 + -45 x = 56.789083458 + -45 Combine like terms: 56.789083458 + -45 = 11.789083458 x = 11.789083458 Simplifying x = 11.789083458Subproblem 2
x + 45 = -56.789083458 Simplifying x + 45 = -56.789083458 Reorder the terms: 45 + x = -56.789083458 Solving 45 + x = -56.789083458 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 = -56.789083458 + -45 Combine like terms: 45 + -45 = 0 0 + x = -56.789083458 + -45 x = -56.789083458 + -45 Combine like terms: -56.789083458 + -45 = -101.789083458 x = -101.789083458 Simplifying x = -101.789083458Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.789083458, -101.789083458}
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