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Simplifying 75 = 14x + 2x2 Solving 75 = 14x + 2x2 Solving for variable 'x'. Reorder the terms: 75 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2 Combine like terms: 14x + -14x = 0 75 + -14x + -2x2 = 0 + 2x2 + -2x2 75 + -14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 75 + -14x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -37.5 + 7x + x2 = 0 Move the constant term to the right: Add '37.5' to each side of the equation. -37.5 + 7x + 37.5 + x2 = 0 + 37.5 Reorder the terms: -37.5 + 37.5 + 7x + x2 = 0 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + 7x + x2 = 0 + 37.5 7x + x2 = 0 + 37.5 Combine like terms: 0 + 37.5 = 37.5 7x + x2 = 37.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 37.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 37.5 + 12.25 Combine like terms: 37.5 + 12.25 = 49.75 12.25 + 7x + x2 = 49.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 49.75 Calculate the square root of the right side: 7.05336799 Break this problem into two subproblems by setting (x + 3.5) equal to 7.05336799 and -7.05336799.Subproblem 1
x + 3.5 = 7.05336799 Simplifying x + 3.5 = 7.05336799 Reorder the terms: 3.5 + x = 7.05336799 Solving 3.5 + x = 7.05336799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 7.05336799 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 7.05336799 + -3.5 x = 7.05336799 + -3.5 Combine like terms: 7.05336799 + -3.5 = 3.55336799 x = 3.55336799 Simplifying x = 3.55336799Subproblem 2
x + 3.5 = -7.05336799 Simplifying x + 3.5 = -7.05336799 Reorder the terms: 3.5 + x = -7.05336799 Solving 3.5 + x = -7.05336799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -7.05336799 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -7.05336799 + -3.5 x = -7.05336799 + -3.5 Combine like terms: -7.05336799 + -3.5 = -10.55336799 x = -10.55336799 Simplifying x = -10.55336799Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.55336799, -10.55336799}
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