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Simplifying 51 = x2 + 21x Reorder the terms: 51 = 21x + x2 Solving 51 = 21x + x2 Solving for variable 'x'. Reorder the terms: 51 + -21x + -1x2 = 21x + -21x + x2 + -1x2 Combine like terms: 21x + -21x = 0 51 + -21x + -1x2 = 0 + x2 + -1x2 51 + -21x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 51 + -21x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -51 + 21x + x2 = 0 Move the constant term to the right: Add '51' to each side of the equation. -51 + 21x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + 21x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 21x + x2 = 0 + 51 21x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 21x + x2 = 51 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 = 51 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 51 + 110.25 Combine like terms: 51 + 110.25 = 161.25 110.25 + 21x + x2 = 161.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 161.25 Calculate the square root of the right side: 12.698425099 Break this problem into two subproblems by setting (x + 10.5) equal to 12.698425099 and -12.698425099.Subproblem 1
x + 10.5 = 12.698425099 Simplifying x + 10.5 = 12.698425099 Reorder the terms: 10.5 + x = 12.698425099 Solving 10.5 + x = 12.698425099 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 = 12.698425099 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 12.698425099 + -10.5 x = 12.698425099 + -10.5 Combine like terms: 12.698425099 + -10.5 = 2.198425099 x = 2.198425099 Simplifying x = 2.198425099Subproblem 2
x + 10.5 = -12.698425099 Simplifying x + 10.5 = -12.698425099 Reorder the terms: 10.5 + x = -12.698425099 Solving 10.5 + x = -12.698425099 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 = -12.698425099 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -12.698425099 + -10.5 x = -12.698425099 + -10.5 Combine like terms: -12.698425099 + -10.5 = -23.198425099 x = -23.198425099 Simplifying x = -23.198425099Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.198425099, -23.198425099}
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