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Simplifying x2 = 21x + -22 Reorder the terms: x2 = -22 + 21x Solving x2 = -22 + 21x Solving for variable 'x'. Reorder the terms: 22 + -21x + x2 = -22 + 21x + 22 + -21x Reorder the terms: 22 + -21x + x2 = -22 + 22 + 21x + -21x Combine like terms: -22 + 22 = 0 22 + -21x + x2 = 0 + 21x + -21x 22 + -21x + x2 = 21x + -21x Combine like terms: 21x + -21x = 0 22 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -21x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + -21x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -21x + x2 = 0 + -22 -21x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 -21x + x2 = -22 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 = -22 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -22 + 110.25 Combine like terms: -22 + 110.25 = 88.25 110.25 + -21x + x2 = 88.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 88.25 Calculate the square root of the right side: 9.394147114 Break this problem into two subproblems by setting (x + -10.5) equal to 9.394147114 and -9.394147114.Subproblem 1
x + -10.5 = 9.394147114 Simplifying x + -10.5 = 9.394147114 Reorder the terms: -10.5 + x = 9.394147114 Solving -10.5 + x = 9.394147114 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 = 9.394147114 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 9.394147114 + 10.5 x = 9.394147114 + 10.5 Combine like terms: 9.394147114 + 10.5 = 19.894147114 x = 19.894147114 Simplifying x = 19.894147114Subproblem 2
x + -10.5 = -9.394147114 Simplifying x + -10.5 = -9.394147114 Reorder the terms: -10.5 + x = -9.394147114 Solving -10.5 + x = -9.394147114 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 = -9.394147114 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -9.394147114 + 10.5 x = -9.394147114 + 10.5 Combine like terms: -9.394147114 + 10.5 = 1.105852886 x = 1.105852886 Simplifying x = 1.105852886Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.894147114, 1.105852886}
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