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Simplifying x2 + -21x + 72 = 0 Reorder the terms: 72 + -21x + x2 = 0 Solving 72 + -21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + -21x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + -21x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -21x + x2 = 0 + -72 -21x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 -21x + x2 = -72 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 = -72 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -72 + 110.25 Combine like terms: -72 + 110.25 = 38.25 110.25 + -21x + x2 = 38.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (x + -10.5) equal to 6.184658438 and -6.184658438.Subproblem 1
x + -10.5 = 6.184658438 Simplifying x + -10.5 = 6.184658438 Reorder the terms: -10.5 + x = 6.184658438 Solving -10.5 + x = 6.184658438 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 = 6.184658438 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 6.184658438 + 10.5 x = 6.184658438 + 10.5 Combine like terms: 6.184658438 + 10.5 = 16.684658438 x = 16.684658438 Simplifying x = 16.684658438Subproblem 2
x + -10.5 = -6.184658438 Simplifying x + -10.5 = -6.184658438 Reorder the terms: -10.5 + x = -6.184658438 Solving -10.5 + x = -6.184658438 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 = -6.184658438 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -6.184658438 + 10.5 x = -6.184658438 + 10.5 Combine like terms: -6.184658438 + 10.5 = 4.315341562 x = 4.315341562 Simplifying x = 4.315341562Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.684658438, 4.315341562}
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