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Simplifying 20x + 51 = x2 Reorder the terms: 51 + 20x = x2 Solving 51 + 20x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 51 + 20x + -1x2 = 0 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 = 22.288205727 x = 22.288205727 Simplifying x = 22.288205727Subproblem 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 = -2.288205727 x = -2.288205727 Simplifying x = -2.288205727Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.288205727, -2.288205727}
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