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Simplifying x2 + 90x + -36 = 0 Reorder the terms: -36 + 90x + x2 = 0 Solving -36 + 90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 90x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 90x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 90x + x2 = 0 + 36 90x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 90x + x2 = 36 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 = 36 + 2025 Reorder the terms: 2025 + 90x + x2 = 36 + 2025 Combine like terms: 36 + 2025 = 2061 2025 + 90x + x2 = 2061 Factor a perfect square on the left side: (x + 45)(x + 45) = 2061 Calculate the square root of the right side: 45.398237851 Break this problem into two subproblems by setting (x + 45) equal to 45.398237851 and -45.398237851.Subproblem 1
x + 45 = 45.398237851 Simplifying x + 45 = 45.398237851 Reorder the terms: 45 + x = 45.398237851 Solving 45 + x = 45.398237851 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 = 45.398237851 + -45 Combine like terms: 45 + -45 = 0 0 + x = 45.398237851 + -45 x = 45.398237851 + -45 Combine like terms: 45.398237851 + -45 = 0.398237851 x = 0.398237851 Simplifying x = 0.398237851Subproblem 2
x + 45 = -45.398237851 Simplifying x + 45 = -45.398237851 Reorder the terms: 45 + x = -45.398237851 Solving 45 + x = -45.398237851 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 = -45.398237851 + -45 Combine like terms: 45 + -45 = 0 0 + x = -45.398237851 + -45 x = -45.398237851 + -45 Combine like terms: -45.398237851 + -45 = -90.398237851 x = -90.398237851 Simplifying x = -90.398237851Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.398237851, -90.398237851}
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