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Simplifying 2X2 + 20X = -21 Reorder the terms: 20X + 2X2 = -21 Solving 20X + 2X2 = -21 Solving for variable 'X'. Reorder the terms: 21 + 20X + 2X2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + 20X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + 10X + X2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + 10X + -10.5 + X2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + 10X + X2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + 10X + X2 = 0 + -10.5 10X + X2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 10X + X2 = -10.5 The X term is 10X. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10X + 25 + X2 = -10.5 + 25 Reorder the terms: 25 + 10X + X2 = -10.5 + 25 Combine like terms: -10.5 + 25 = 14.5 25 + 10X + X2 = 14.5 Factor a perfect square on the left side: (X + 5)(X + 5) = 14.5 Calculate the square root of the right side: 3.807886553 Break this problem into two subproblems by setting (X + 5) equal to 3.807886553 and -3.807886553.Subproblem 1
X + 5 = 3.807886553 Simplifying X + 5 = 3.807886553 Reorder the terms: 5 + X = 3.807886553 Solving 5 + X = 3.807886553 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + X = 3.807886553 + -5 Combine like terms: 5 + -5 = 0 0 + X = 3.807886553 + -5 X = 3.807886553 + -5 Combine like terms: 3.807886553 + -5 = -1.192113447 X = -1.192113447 Simplifying X = -1.192113447Subproblem 2
X + 5 = -3.807886553 Simplifying X + 5 = -3.807886553 Reorder the terms: 5 + X = -3.807886553 Solving 5 + X = -3.807886553 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + X = -3.807886553 + -5 Combine like terms: 5 + -5 = 0 0 + X = -3.807886553 + -5 X = -3.807886553 + -5 Combine like terms: -3.807886553 + -5 = -8.807886553 X = -8.807886553 Simplifying X = -8.807886553Solution
The solution to the problem is based on the solutions from the subproblems. X = {-1.192113447, -8.807886553}
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