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Simplifying x2 + -90x + 324 = 0 Reorder the terms: 324 + -90x + x2 = 0 Solving 324 + -90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-324' to each side of the equation. 324 + -90x + -324 + x2 = 0 + -324 Reorder the terms: 324 + -324 + -90x + x2 = 0 + -324 Combine like terms: 324 + -324 = 0 0 + -90x + x2 = 0 + -324 -90x + x2 = 0 + -324 Combine like terms: 0 + -324 = -324 -90x + x2 = -324 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 = -324 + 2025 Reorder the terms: 2025 + -90x + x2 = -324 + 2025 Combine like terms: -324 + 2025 = 1701 2025 + -90x + x2 = 1701 Factor a perfect square on the left side: (x + -45)(x + -45) = 1701 Calculate the square root of the right side: 41.243181255 Break this problem into two subproblems by setting (x + -45) equal to 41.243181255 and -41.243181255.Subproblem 1
x + -45 = 41.243181255 Simplifying x + -45 = 41.243181255 Reorder the terms: -45 + x = 41.243181255 Solving -45 + x = 41.243181255 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 = 41.243181255 + 45 Combine like terms: -45 + 45 = 0 0 + x = 41.243181255 + 45 x = 41.243181255 + 45 Combine like terms: 41.243181255 + 45 = 86.243181255 x = 86.243181255 Simplifying x = 86.243181255Subproblem 2
x + -45 = -41.243181255 Simplifying x + -45 = -41.243181255 Reorder the terms: -45 + x = -41.243181255 Solving -45 + x = -41.243181255 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 = -41.243181255 + 45 Combine like terms: -45 + 45 = 0 0 + x = -41.243181255 + 45 x = -41.243181255 + 45 Combine like terms: -41.243181255 + 45 = 3.756818745 x = 3.756818745 Simplifying x = 3.756818745Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.243181255, 3.756818745}
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