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Simplifying x(x + 7) = 20 Reorder the terms: x(7 + x) = 20 (7 * x + x * x) = 20 (7x + x2) = 20 Solving 7x + x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 7x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 7x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 7x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 7x + x2 = 0 + 20 7x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 7x + x2 = 20 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 = 20 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 20 + 12.25 Combine like terms: 20 + 12.25 = 32.25 12.25 + 7x + x2 = 32.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + 3.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + 3.5 = 5.678908346 Simplifying x + 3.5 = 5.678908346 Reorder the terms: 3.5 + x = 5.678908346 Solving 3.5 + x = 5.678908346 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 = 5.678908346 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.678908346 + -3.5 x = 5.678908346 + -3.5 Combine like terms: 5.678908346 + -3.5 = 2.178908346 x = 2.178908346 Simplifying x = 2.178908346Subproblem 2
x + 3.5 = -5.678908346 Simplifying x + 3.5 = -5.678908346 Reorder the terms: 3.5 + x = -5.678908346 Solving 3.5 + x = -5.678908346 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 = -5.678908346 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.678908346 + -3.5 x = -5.678908346 + -3.5 Combine like terms: -5.678908346 + -3.5 = -9.178908346 x = -9.178908346 Simplifying x = -9.178908346Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.178908346, -9.178908346}
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