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Simplifying -1x2 + -20x + 51 = 0 Reorder the terms: 51 + -20x + -1x2 = 0 Solving 51 + -20x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -51 + 20x + x2 = 0 Move the constant term to the right: Add '51' to each side of the equation. -51 + 20x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + 20x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + 20x + x2 = 0 + 51 20x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 20x + x2 = 51 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 51 + 100 Reorder the terms: 100 + 20x + x2 = 51 + 100 Combine like terms: 51 + 100 = 151 100 + 20x + x2 = 151 Factor a perfect square on the left side: (x + 10)(x + 10) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (x + 10) equal to 12.288205727 and -12.288205727.Subproblem 1
x + 10 = 12.288205727 Simplifying x + 10 = 12.288205727 Reorder the terms: 10 + x = 12.288205727 Solving 10 + x = 12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 12.288205727 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.288205727 + -10 x = 12.288205727 + -10 Combine like terms: 12.288205727 + -10 = 2.288205727 x = 2.288205727 Simplifying x = 2.288205727Subproblem 2
x + 10 = -12.288205727 Simplifying x + 10 = -12.288205727 Reorder the terms: 10 + x = -12.288205727 Solving 10 + x = -12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -12.288205727 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.288205727 + -10 x = -12.288205727 + -10 Combine like terms: -12.288205727 + -10 = -22.288205727 x = -22.288205727 Simplifying x = -22.288205727Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.288205727, -22.288205727}
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