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Simplifying x2 + 7x = 52 Reorder the terms: 7x + x2 = 52 Solving 7x + x2 = 52 Solving for variable 'x'. Reorder the terms: -52 + 7x + x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 7x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 7x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 7x + x2 = 0 + 52 7x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 7x + x2 = 52 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 = 52 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 52 + 12.25 Combine like terms: 52 + 12.25 = 64.25 12.25 + 7x + x2 = 64.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (x + 3.5) equal to 8.015609771 and -8.015609771.Subproblem 1
x + 3.5 = 8.015609771 Simplifying x + 3.5 = 8.015609771 Reorder the terms: 3.5 + x = 8.015609771 Solving 3.5 + x = 8.015609771 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 = 8.015609771 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 8.015609771 + -3.5 x = 8.015609771 + -3.5 Combine like terms: 8.015609771 + -3.5 = 4.515609771 x = 4.515609771 Simplifying x = 4.515609771Subproblem 2
x + 3.5 = -8.015609771 Simplifying x + 3.5 = -8.015609771 Reorder the terms: 3.5 + x = -8.015609771 Solving 3.5 + x = -8.015609771 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 = -8.015609771 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -8.015609771 + -3.5 x = -8.015609771 + -3.5 Combine like terms: -8.015609771 + -3.5 = -11.515609771 x = -11.515609771 Simplifying x = -11.515609771Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.515609771, -11.515609771}
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