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Simplifying x2 + -21x + 105 = 0 Reorder the terms: 105 + -21x + x2 = 0 Solving 105 + -21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-105' to each side of the equation. 105 + -21x + -105 + x2 = 0 + -105 Reorder the terms: 105 + -105 + -21x + x2 = 0 + -105 Combine like terms: 105 + -105 = 0 0 + -21x + x2 = 0 + -105 -21x + x2 = 0 + -105 Combine like terms: 0 + -105 = -105 -21x + x2 = -105 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 = -105 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -105 + 110.25 Combine like terms: -105 + 110.25 = 5.25 110.25 + -21x + x2 = 5.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -10.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + -10.5 = 2.291287847 Simplifying x + -10.5 = 2.291287847 Reorder the terms: -10.5 + x = 2.291287847 Solving -10.5 + x = 2.291287847 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 = 2.291287847 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 2.291287847 + 10.5 x = 2.291287847 + 10.5 Combine like terms: 2.291287847 + 10.5 = 12.791287847 x = 12.791287847 Simplifying x = 12.791287847Subproblem 2
x + -10.5 = -2.291287847 Simplifying x + -10.5 = -2.291287847 Reorder the terms: -10.5 + x = -2.291287847 Solving -10.5 + x = -2.291287847 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 = -2.291287847 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -2.291287847 + 10.5 x = -2.291287847 + 10.5 Combine like terms: -2.291287847 + 10.5 = 8.208712153 x = 8.208712153 Simplifying x = 8.208712153Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.791287847, 8.208712153}
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