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Simplifying x2 + -75x + 325 = 0 Reorder the terms: 325 + -75x + x2 = 0 Solving 325 + -75x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-325' to each side of the equation. 325 + -75x + -325 + x2 = 0 + -325 Reorder the terms: 325 + -325 + -75x + x2 = 0 + -325 Combine like terms: 325 + -325 = 0 0 + -75x + x2 = 0 + -325 -75x + x2 = 0 + -325 Combine like terms: 0 + -325 = -325 -75x + x2 = -325 The x term is -75x. Take half its coefficient (-37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. -75x + 1406.25 + x2 = -325 + 1406.25 Reorder the terms: 1406.25 + -75x + x2 = -325 + 1406.25 Combine like terms: -325 + 1406.25 = 1081.25 1406.25 + -75x + x2 = 1081.25 Factor a perfect square on the left side: (x + -37.5)(x + -37.5) = 1081.25 Calculate the square root of the right side: 32.882366095 Break this problem into two subproblems by setting (x + -37.5) equal to 32.882366095 and -32.882366095.Subproblem 1
x + -37.5 = 32.882366095 Simplifying x + -37.5 = 32.882366095 Reorder the terms: -37.5 + x = 32.882366095 Solving -37.5 + x = 32.882366095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = 32.882366095 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 32.882366095 + 37.5 x = 32.882366095 + 37.5 Combine like terms: 32.882366095 + 37.5 = 70.382366095 x = 70.382366095 Simplifying x = 70.382366095Subproblem 2
x + -37.5 = -32.882366095 Simplifying x + -37.5 = -32.882366095 Reorder the terms: -37.5 + x = -32.882366095 Solving -37.5 + x = -32.882366095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = -32.882366095 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = -32.882366095 + 37.5 x = -32.882366095 + 37.5 Combine like terms: -32.882366095 + 37.5 = 4.617633905 x = 4.617633905 Simplifying x = 4.617633905Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.382366095, 4.617633905}
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