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Simplifying 3.5x2 + 700x + -15400 = 0 Reorder the terms: -15400 + 700x + 3.5x2 = 0 Solving -15400 + 700x + 3.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. -4400 + 200x + x2 = 0 Move the constant term to the right: Add '4400' to each side of the equation. -4400 + 200x + 4400 + x2 = 0 + 4400 Reorder the terms: -4400 + 4400 + 200x + x2 = 0 + 4400 Combine like terms: -4400 + 4400 = 0 0 + 200x + x2 = 0 + 4400 200x + x2 = 0 + 4400 Combine like terms: 0 + 4400 = 4400 200x + x2 = 4400 The x term is 200x. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200x + 10000 + x2 = 4400 + 10000 Reorder the terms: 10000 + 200x + x2 = 4400 + 10000 Combine like terms: 4400 + 10000 = 14400 10000 + 200x + x2 = 14400 Factor a perfect square on the left side: (x + 100)(x + 100) = 14400 Calculate the square root of the right side: 120 Break this problem into two subproblems by setting (x + 100) equal to 120 and -120.Subproblem 1
x + 100 = 120 Simplifying x + 100 = 120 Reorder the terms: 100 + x = 120 Solving 100 + x = 120 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = 120 + -100 Combine like terms: 100 + -100 = 0 0 + x = 120 + -100 x = 120 + -100 Combine like terms: 120 + -100 = 20 x = 20 Simplifying x = 20Subproblem 2
x + 100 = -120 Simplifying x + 100 = -120 Reorder the terms: 100 + x = -120 Solving 100 + x = -120 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + x = -120 + -100 Combine like terms: 100 + -100 = 0 0 + x = -120 + -100 x = -120 + -100 Combine like terms: -120 + -100 = -220 x = -220 Simplifying x = -220Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -220}
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