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Simplifying x2 + 7x = 34 Reorder the terms: 7x + x2 = 34 Solving 7x + x2 = 34 Solving for variable 'x'. Reorder the terms: -34 + 7x + x2 = 34 + -34 Combine like terms: 34 + -34 = 0 -34 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + 7x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + 7x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + 7x + x2 = 0 + 34 7x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 7x + x2 = 34 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 = 34 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 34 + 12.25 Combine like terms: 34 + 12.25 = 46.25 12.25 + 7x + x2 = 46.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (x + 3.5) equal to 6.800735254 and -6.800735254.Subproblem 1
x + 3.5 = 6.800735254 Simplifying x + 3.5 = 6.800735254 Reorder the terms: 3.5 + x = 6.800735254 Solving 3.5 + x = 6.800735254 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 = 6.800735254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.800735254 + -3.5 x = 6.800735254 + -3.5 Combine like terms: 6.800735254 + -3.5 = 3.300735254 x = 3.300735254 Simplifying x = 3.300735254Subproblem 2
x + 3.5 = -6.800735254 Simplifying x + 3.5 = -6.800735254 Reorder the terms: 3.5 + x = -6.800735254 Solving 3.5 + x = -6.800735254 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 = -6.800735254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.800735254 + -3.5 x = -6.800735254 + -3.5 Combine like terms: -6.800735254 + -3.5 = -10.300735254 x = -10.300735254 Simplifying x = -10.300735254Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.300735254, -10.300735254}
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