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Simplifying 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 = 8.807886553 x = 8.807886553 Simplifying x = 8.807886553Subproblem 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 = 1.192113447 x = 1.192113447 Simplifying x = 1.192113447Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.807886553, 1.192113447}
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