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Simplifying x2 + -90x + -3 = 0 Reorder the terms: -3 + -90x + x2 = 0 Solving -3 + -90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -90x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -90x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -90x + x2 = 0 + 3 -90x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -90x + x2 = 3 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 = 3 + 2025 Reorder the terms: 2025 + -90x + x2 = 3 + 2025 Combine like terms: 3 + 2025 = 2028 2025 + -90x + x2 = 2028 Factor a perfect square on the left side: (x + -45)(x + -45) = 2028 Calculate the square root of the right side: 45.033320997 Break this problem into two subproblems by setting (x + -45) equal to 45.033320997 and -45.033320997.Subproblem 1
x + -45 = 45.033320997 Simplifying x + -45 = 45.033320997 Reorder the terms: -45 + x = 45.033320997 Solving -45 + x = 45.033320997 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 = 45.033320997 + 45 Combine like terms: -45 + 45 = 0 0 + x = 45.033320997 + 45 x = 45.033320997 + 45 Combine like terms: 45.033320997 + 45 = 90.033320997 x = 90.033320997 Simplifying x = 90.033320997Subproblem 2
x + -45 = -45.033320997 Simplifying x + -45 = -45.033320997 Reorder the terms: -45 + x = -45.033320997 Solving -45 + x = -45.033320997 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 = -45.033320997 + 45 Combine like terms: -45 + 45 = 0 0 + x = -45.033320997 + 45 x = -45.033320997 + 45 Combine like terms: -45.033320997 + 45 = -0.033320997 x = -0.033320997 Simplifying x = -0.033320997Solution
The solution to the problem is based on the solutions from the subproblems. x = {90.033320997, -0.033320997}
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