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Simplifying x2 + 7x = 225 Reorder the terms: 7x + x2 = 225 Solving 7x + x2 = 225 Solving for variable 'x'. Reorder the terms: -225 + 7x + x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -225 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 7x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 7x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 7x + x2 = 0 + 225 7x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 7x + x2 = 225 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 225 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 225 + 12.25 Combine like terms: 225 + 12.25 = 237.25 12.25 + 7x + x2 = 237.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 237.25 Calculate the square root of the right side: 15.402921801 Break this problem into two subproblems by setting (x + 3.5) equal to 15.402921801 and -15.402921801.Subproblem 1
x + 3.5 = 15.402921801 Simplifying x + 3.5 = 15.402921801 Reorder the terms: 3.5 + x = 15.402921801 Solving 3.5 + x = 15.402921801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 15.402921801 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 15.402921801 + -3.5 x = 15.402921801 + -3.5 Combine like terms: 15.402921801 + -3.5 = 11.902921801 x = 11.902921801 Simplifying x = 11.902921801Subproblem 2
x + 3.5 = -15.402921801 Simplifying x + 3.5 = -15.402921801 Reorder the terms: 3.5 + x = -15.402921801 Solving 3.5 + x = -15.402921801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -15.402921801 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -15.402921801 + -3.5 x = -15.402921801 + -3.5 Combine like terms: -15.402921801 + -3.5 = -18.902921801 x = -18.902921801 Simplifying x = -18.902921801Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.902921801, -18.902921801}
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