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Simplifying x(x + 7) = 56 Reorder the terms: x(7 + x) = 56 (7 * x + x * x) = 56 (7x + x2) = 56 Solving 7x + x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + 7x + x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 7x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 7x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 7x + x2 = 0 + 56 7x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 7x + x2 = 56 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 = 56 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 56 + 12.25 Combine like terms: 56 + 12.25 = 68.25 12.25 + 7x + x2 = 68.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + 3.5) equal to 8.261355821 and -8.261355821.Subproblem 1
x + 3.5 = 8.261355821 Simplifying x + 3.5 = 8.261355821 Reorder the terms: 3.5 + x = 8.261355821 Solving 3.5 + x = 8.261355821 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 = 8.261355821 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 8.261355821 + -3.5 x = 8.261355821 + -3.5 Combine like terms: 8.261355821 + -3.5 = 4.761355821 x = 4.761355821 Simplifying x = 4.761355821Subproblem 2
x + 3.5 = -8.261355821 Simplifying x + 3.5 = -8.261355821 Reorder the terms: 3.5 + x = -8.261355821 Solving 3.5 + x = -8.261355821 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 = -8.261355821 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -8.261355821 + -3.5 x = -8.261355821 + -3.5 Combine like terms: -8.261355821 + -3.5 = -11.761355821 x = -11.761355821 Simplifying x = -11.761355821Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.761355821, -11.761355821}
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