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Simplifying x2 + -90x + 20.25 = 0 Reorder the terms: 20.25 + -90x + x2 = 0 Solving 20.25 + -90x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-20.25' to each side of the equation. 20.25 + -90x + -20.25 + x2 = 0 + -20.25 Reorder the terms: 20.25 + -20.25 + -90x + x2 = 0 + -20.25 Combine like terms: 20.25 + -20.25 = 0.00 0.00 + -90x + x2 = 0 + -20.25 -90x + x2 = 0 + -20.25 Combine like terms: 0 + -20.25 = -20.25 -90x + x2 = -20.25 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 = -20.25 + 2025 Reorder the terms: 2025 + -90x + x2 = -20.25 + 2025 Combine like terms: -20.25 + 2025 = 2004.75 2025 + -90x + x2 = 2004.75 Factor a perfect square on the left side: (x + -45)(x + -45) = 2004.75 Calculate the square root of the right side: 44.77443467 Break this problem into two subproblems by setting (x + -45) equal to 44.77443467 and -44.77443467.Subproblem 1
x + -45 = 44.77443467 Simplifying x + -45 = 44.77443467 Reorder the terms: -45 + x = 44.77443467 Solving -45 + x = 44.77443467 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 = 44.77443467 + 45 Combine like terms: -45 + 45 = 0 0 + x = 44.77443467 + 45 x = 44.77443467 + 45 Combine like terms: 44.77443467 + 45 = 89.77443467 x = 89.77443467 Simplifying x = 89.77443467Subproblem 2
x + -45 = -44.77443467 Simplifying x + -45 = -44.77443467 Reorder the terms: -45 + x = -44.77443467 Solving -45 + x = -44.77443467 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 = -44.77443467 + 45 Combine like terms: -45 + 45 = 0 0 + x = -44.77443467 + 45 x = -44.77443467 + 45 Combine like terms: -44.77443467 + 45 = 0.22556533 x = 0.22556533 Simplifying x = 0.22556533Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.77443467, 0.22556533}
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