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Simplifying 4x2 + 80x + 275 = 0 Reorder the terms: 275 + 80x + 4x2 = 0 Solving 275 + 80x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 68.75 + 20x + x2 = 0 Move the constant term to the right: Add '-68.75' to each side of the equation. 68.75 + 20x + -68.75 + x2 = 0 + -68.75 Reorder the terms: 68.75 + -68.75 + 20x + x2 = 0 + -68.75 Combine like terms: 68.75 + -68.75 = 0.00 0.00 + 20x + x2 = 0 + -68.75 20x + x2 = 0 + -68.75 Combine like terms: 0 + -68.75 = -68.75 20x + x2 = -68.75 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 = -68.75 + 100 Reorder the terms: 100 + 20x + x2 = -68.75 + 100 Combine like terms: -68.75 + 100 = 31.25 100 + 20x + x2 = 31.25 Factor a perfect square on the left side: (x + 10)(x + 10) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + 10) equal to 5.590169944 and -5.590169944.Subproblem 1
x + 10 = 5.590169944 Simplifying x + 10 = 5.590169944 Reorder the terms: 10 + x = 5.590169944 Solving 10 + x = 5.590169944 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 = 5.590169944 + -10 Combine like terms: 10 + -10 = 0 0 + x = 5.590169944 + -10 x = 5.590169944 + -10 Combine like terms: 5.590169944 + -10 = -4.409830056 x = -4.409830056 Simplifying x = -4.409830056Subproblem 2
x + 10 = -5.590169944 Simplifying x + 10 = -5.590169944 Reorder the terms: 10 + x = -5.590169944 Solving 10 + x = -5.590169944 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 = -5.590169944 + -10 Combine like terms: 10 + -10 = 0 0 + x = -5.590169944 + -10 x = -5.590169944 + -10 Combine like terms: -5.590169944 + -10 = -15.590169944 x = -15.590169944 Simplifying x = -15.590169944Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.409830056, -15.590169944}
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