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Simplifying x2 + 7x + 10 = 315 Reorder the terms: 10 + 7x + x2 = 315 Solving 10 + 7x + x2 = 315 Solving for variable 'x'. Reorder the terms: 10 + -315 + 7x + x2 = 315 + -315 Combine like terms: 10 + -315 = -305 -305 + 7x + x2 = 315 + -315 Combine like terms: 315 + -315 = 0 -305 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '305' to each side of the equation. -305 + 7x + 305 + x2 = 0 + 305 Reorder the terms: -305 + 305 + 7x + x2 = 0 + 305 Combine like terms: -305 + 305 = 0 0 + 7x + x2 = 0 + 305 7x + x2 = 0 + 305 Combine like terms: 0 + 305 = 305 7x + x2 = 305 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 = 305 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 305 + 12.25 Combine like terms: 305 + 12.25 = 317.25 12.25 + 7x + x2 = 317.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 317.25 Calculate the square root of the right side: 17.811513131 Break this problem into two subproblems by setting (x + 3.5) equal to 17.811513131 and -17.811513131.Subproblem 1
x + 3.5 = 17.811513131 Simplifying x + 3.5 = 17.811513131 Reorder the terms: 3.5 + x = 17.811513131 Solving 3.5 + x = 17.811513131 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 = 17.811513131 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 17.811513131 + -3.5 x = 17.811513131 + -3.5 Combine like terms: 17.811513131 + -3.5 = 14.311513131 x = 14.311513131 Simplifying x = 14.311513131Subproblem 2
x + 3.5 = -17.811513131 Simplifying x + 3.5 = -17.811513131 Reorder the terms: 3.5 + x = -17.811513131 Solving 3.5 + x = -17.811513131 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 = -17.811513131 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -17.811513131 + -3.5 x = -17.811513131 + -3.5 Combine like terms: -17.811513131 + -3.5 = -21.311513131 x = -21.311513131 Simplifying x = -21.311513131Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.311513131, -21.311513131}
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