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Simplifying x2 + -20x + 76 = 0 Reorder the terms: 76 + -20x + x2 = 0 Solving 76 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-76' to each side of the equation. 76 + -20x + -76 + x2 = 0 + -76 Reorder the terms: 76 + -76 + -20x + x2 = 0 + -76 Combine like terms: 76 + -76 = 0 0 + -20x + x2 = 0 + -76 -20x + x2 = 0 + -76 Combine like terms: 0 + -76 = -76 -20x + x2 = -76 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 = -76 + 100 Reorder the terms: 100 + -20x + x2 = -76 + 100 Combine like terms: -76 + 100 = 24 100 + -20x + x2 = 24 Factor a perfect square on the left side: (x + -10)(x + -10) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -10) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -10 = 4.898979486 Simplifying x + -10 = 4.898979486 Reorder the terms: -10 + x = 4.898979486 Solving -10 + x = 4.898979486 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 = 4.898979486 + 10 Combine like terms: -10 + 10 = 0 0 + x = 4.898979486 + 10 x = 4.898979486 + 10 Combine like terms: 4.898979486 + 10 = 14.898979486 x = 14.898979486 Simplifying x = 14.898979486Subproblem 2
x + -10 = -4.898979486 Simplifying x + -10 = -4.898979486 Reorder the terms: -10 + x = -4.898979486 Solving -10 + x = -4.898979486 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 = -4.898979486 + 10 Combine like terms: -10 + 10 = 0 0 + x = -4.898979486 + 10 x = -4.898979486 + 10 Combine like terms: -4.898979486 + 10 = 5.101020514 x = 5.101020514 Simplifying x = 5.101020514Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.898979486, 5.101020514}
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