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Simplifying x2 + -90x + 90 = 0 Reorder the terms: 90 + -90x + x2 = 0 Solving 90 + -90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + -90x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + -90x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -90x + x2 = 0 + -90 -90x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 -90x + x2 = -90 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 = -90 + 2025 Reorder the terms: 2025 + -90x + x2 = -90 + 2025 Combine like terms: -90 + 2025 = 1935 2025 + -90x + x2 = 1935 Factor a perfect square on the left side: (x + -45)(x + -45) = 1935 Calculate the square root of the right side: 43.988634896 Break this problem into two subproblems by setting (x + -45) equal to 43.988634896 and -43.988634896.Subproblem 1
x + -45 = 43.988634896 Simplifying x + -45 = 43.988634896 Reorder the terms: -45 + x = 43.988634896 Solving -45 + x = 43.988634896 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 = 43.988634896 + 45 Combine like terms: -45 + 45 = 0 0 + x = 43.988634896 + 45 x = 43.988634896 + 45 Combine like terms: 43.988634896 + 45 = 88.988634896 x = 88.988634896 Simplifying x = 88.988634896Subproblem 2
x + -45 = -43.988634896 Simplifying x + -45 = -43.988634896 Reorder the terms: -45 + x = -43.988634896 Solving -45 + x = -43.988634896 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 = -43.988634896 + 45 Combine like terms: -45 + 45 = 0 0 + x = -43.988634896 + 45 x = -43.988634896 + 45 Combine like terms: -43.988634896 + 45 = 1.011365104 x = 1.011365104 Simplifying x = 1.011365104Solution
The solution to the problem is based on the solutions from the subproblems. x = {88.988634896, 1.011365104}
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