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Simplifying x2 + 7x = 6084 Reorder the terms: 7x + x2 = 6084 Solving 7x + x2 = 6084 Solving for variable 'x'. Reorder the terms: -6084 + 7x + x2 = 6084 + -6084 Combine like terms: 6084 + -6084 = 0 -6084 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6084' to each side of the equation. -6084 + 7x + 6084 + x2 = 0 + 6084 Reorder the terms: -6084 + 6084 + 7x + x2 = 0 + 6084 Combine like terms: -6084 + 6084 = 0 0 + 7x + x2 = 0 + 6084 7x + x2 = 0 + 6084 Combine like terms: 0 + 6084 = 6084 7x + x2 = 6084 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 = 6084 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 6084 + 12.25 Combine like terms: 6084 + 12.25 = 6096.25 12.25 + 7x + x2 = 6096.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 6096.25 Calculate the square root of the right side: 78.078486153 Break this problem into two subproblems by setting (x + 3.5) equal to 78.078486153 and -78.078486153.Subproblem 1
x + 3.5 = 78.078486153 Simplifying x + 3.5 = 78.078486153 Reorder the terms: 3.5 + x = 78.078486153 Solving 3.5 + x = 78.078486153 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 = 78.078486153 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 78.078486153 + -3.5 x = 78.078486153 + -3.5 Combine like terms: 78.078486153 + -3.5 = 74.578486153 x = 74.578486153 Simplifying x = 74.578486153Subproblem 2
x + 3.5 = -78.078486153 Simplifying x + 3.5 = -78.078486153 Reorder the terms: 3.5 + x = -78.078486153 Solving 3.5 + x = -78.078486153 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 = -78.078486153 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -78.078486153 + -3.5 x = -78.078486153 + -3.5 Combine like terms: -78.078486153 + -3.5 = -81.578486153 x = -81.578486153 Simplifying x = -81.578486153Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.578486153, -81.578486153}
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