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Simplifying x2 + 7x = 68.75 Reorder the terms: 7x + x2 = 68.75 Solving 7x + x2 = 68.75 Solving for variable 'x'. Reorder the terms: -68.75 + 7x + x2 = 68.75 + -68.75 Combine like terms: 68.75 + -68.75 = 0.00 -68.75 + 7x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '68.75' to each side of the equation. -68.75 + 7x + 68.75 + x2 = 0.00 + 68.75 Reorder the terms: -68.75 + 68.75 + 7x + x2 = 0.00 + 68.75 Combine like terms: -68.75 + 68.75 = 0.00 0.00 + 7x + x2 = 0.00 + 68.75 7x + x2 = 0.00 + 68.75 Combine like terms: 0.00 + 68.75 = 68.75 7x + x2 = 68.75 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 = 68.75 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 68.75 + 12.25 Combine like terms: 68.75 + 12.25 = 81 12.25 + 7x + x2 = 81 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 81 Calculate the square root of the right side: 9 Break this problem into two subproblems by setting (x + 3.5) equal to 9 and -9.Subproblem 1
x + 3.5 = 9 Simplifying x + 3.5 = 9 Reorder the terms: 3.5 + x = 9 Solving 3.5 + x = 9 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 = 9 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9 + -3.5 x = 9 + -3.5 Combine like terms: 9 + -3.5 = 5.5 x = 5.5 Simplifying x = 5.5Subproblem 2
x + 3.5 = -9 Simplifying x + 3.5 = -9 Reorder the terms: 3.5 + x = -9 Solving 3.5 + x = -9 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 = -9 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9 + -3.5 x = -9 + -3.5 Combine like terms: -9 + -3.5 = -12.5 x = -12.5 Simplifying x = -12.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.5, -12.5}
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