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Simplifying x2 + 5x = 1900 Reorder the terms: 5x + x2 = 1900 Solving 5x + x2 = 1900 Solving for variable 'x'. Reorder the terms: -1900 + 5x + x2 = 1900 + -1900 Combine like terms: 1900 + -1900 = 0 -1900 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1900' to each side of the equation. -1900 + 5x + 1900 + x2 = 0 + 1900 Reorder the terms: -1900 + 1900 + 5x + x2 = 0 + 1900 Combine like terms: -1900 + 1900 = 0 0 + 5x + x2 = 0 + 1900 5x + x2 = 0 + 1900 Combine like terms: 0 + 1900 = 1900 5x + x2 = 1900 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 1900 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1900 + 6.25 Combine like terms: 1900 + 6.25 = 1906.25 6.25 + 5x + x2 = 1906.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 1906.25 Calculate the square root of the right side: 43.660622991 Break this problem into two subproblems by setting (x + 2.5) equal to 43.660622991 and -43.660622991.Subproblem 1
x + 2.5 = 43.660622991 Simplifying x + 2.5 = 43.660622991 Reorder the terms: 2.5 + x = 43.660622991 Solving 2.5 + x = 43.660622991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 43.660622991 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 43.660622991 + -2.5 x = 43.660622991 + -2.5 Combine like terms: 43.660622991 + -2.5 = 41.160622991 x = 41.160622991 Simplifying x = 41.160622991Subproblem 2
x + 2.5 = -43.660622991 Simplifying x + 2.5 = -43.660622991 Reorder the terms: 2.5 + x = -43.660622991 Solving 2.5 + x = -43.660622991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -43.660622991 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -43.660622991 + -2.5 x = -43.660622991 + -2.5 Combine like terms: -43.660622991 + -2.5 = -46.160622991 x = -46.160622991 Simplifying x = -46.160622991Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.160622991, -46.160622991}
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