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Simplifying x2 + -21x + 75 = 0 Reorder the terms: 75 + -21x + x2 = 0 Solving 75 + -21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + -21x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + -21x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -21x + x2 = 0 + -75 -21x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 -21x + x2 = -75 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -75 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -75 + 110.25 Combine like terms: -75 + 110.25 = 35.25 110.25 + -21x + x2 = 35.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + -10.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + -10.5 = 5.937171044 Simplifying x + -10.5 = 5.937171044 Reorder the terms: -10.5 + x = 5.937171044 Solving -10.5 + x = 5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 5.937171044 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 5.937171044 + 10.5 x = 5.937171044 + 10.5 Combine like terms: 5.937171044 + 10.5 = 16.437171044 x = 16.437171044 Simplifying x = 16.437171044Subproblem 2
x + -10.5 = -5.937171044 Simplifying x + -10.5 = -5.937171044 Reorder the terms: -10.5 + x = -5.937171044 Solving -10.5 + x = -5.937171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -5.937171044 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -5.937171044 + 10.5 x = -5.937171044 + 10.5 Combine like terms: -5.937171044 + 10.5 = 4.562828956 x = 4.562828956 Simplifying x = 4.562828956Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.437171044, 4.562828956}
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