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Simplifying 300 = x2 + 7x Reorder the terms: 300 = 7x + x2 Solving 300 = 7x + x2 Solving for variable 'x'. Reorder the terms: 300 + -7x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 300 + -7x + -1x2 = 0 + x2 + -1x2 300 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 300 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -300 + 7x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + 7x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 7x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 7x + x2 = 0 + 300 7x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 7x + x2 = 300 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 = 300 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 300 + 12.25 Combine like terms: 300 + 12.25 = 312.25 12.25 + 7x + x2 = 312.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 312.25 Calculate the square root of the right side: 17.670597047 Break this problem into two subproblems by setting (x + 3.5) equal to 17.670597047 and -17.670597047.Subproblem 1
x + 3.5 = 17.670597047 Simplifying x + 3.5 = 17.670597047 Reorder the terms: 3.5 + x = 17.670597047 Solving 3.5 + x = 17.670597047 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 = 17.670597047 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 17.670597047 + -3.5 x = 17.670597047 + -3.5 Combine like terms: 17.670597047 + -3.5 = 14.170597047 x = 14.170597047 Simplifying x = 14.170597047Subproblem 2
x + 3.5 = -17.670597047 Simplifying x + 3.5 = -17.670597047 Reorder the terms: 3.5 + x = -17.670597047 Solving 3.5 + x = -17.670597047 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 = -17.670597047 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -17.670597047 + -3.5 x = -17.670597047 + -3.5 Combine like terms: -17.670597047 + -3.5 = -21.170597047 x = -21.170597047 Simplifying x = -21.170597047Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.170597047, -21.170597047}
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