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Simplifying x2 + 21 = 12x Reorder the terms: 21 + x2 = 12x Solving 21 + x2 = 12x Solving for variable 'x'. Reorder the terms: 21 + -12x + x2 = 12x + -12x Combine like terms: 12x + -12x = 0 21 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -12x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -12x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -12x + x2 = 0 + -21 -12x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -12x + x2 = -21 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -21 + 36 Reorder the terms: 36 + -12x + x2 = -21 + 36 Combine like terms: -21 + 36 = 15 36 + -12x + x2 = 15 Factor a perfect square on the left side: (x + -6)(x + -6) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -6) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -6 = 3.872983346 Simplifying x + -6 = 3.872983346 Reorder the terms: -6 + x = 3.872983346 Solving -6 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 3.872983346 + 6 Combine like terms: -6 + 6 = 0 0 + x = 3.872983346 + 6 x = 3.872983346 + 6 Combine like terms: 3.872983346 + 6 = 9.872983346 x = 9.872983346 Simplifying x = 9.872983346Subproblem 2
x + -6 = -3.872983346 Simplifying x + -6 = -3.872983346 Reorder the terms: -6 + x = -3.872983346 Solving -6 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -3.872983346 + 6 Combine like terms: -6 + 6 = 0 0 + x = -3.872983346 + 6 x = -3.872983346 + 6 Combine like terms: -3.872983346 + 6 = 2.127016654 x = 2.127016654 Simplifying x = 2.127016654Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.872983346, 2.127016654}
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