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Simplifying x(x + -7) = 91 Reorder the terms: x(-7 + x) = 91 (-7 * x + x * x) = 91 (-7x + x2) = 91 Solving -7x + x2 = 91 Solving for variable 'x'. Reorder the terms: -91 + -7x + x2 = 91 + -91 Combine like terms: 91 + -91 = 0 -91 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + -7x + 91 + x2 = 0 + 91 Reorder the terms: -91 + 91 + -7x + x2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + -7x + x2 = 0 + 91 -7x + x2 = 0 + 91 Combine like terms: 0 + 91 = 91 -7x + x2 = 91 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 = 91 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 91 + 12.25 Combine like terms: 91 + 12.25 = 103.25 12.25 + -7x + x2 = 103.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 103.25 Calculate the square root of the right side: 10.161200716 Break this problem into two subproblems by setting (x + -3.5) equal to 10.161200716 and -10.161200716.Subproblem 1
x + -3.5 = 10.161200716 Simplifying x + -3.5 = 10.161200716 Reorder the terms: -3.5 + x = 10.161200716 Solving -3.5 + x = 10.161200716 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 = 10.161200716 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 10.161200716 + 3.5 x = 10.161200716 + 3.5 Combine like terms: 10.161200716 + 3.5 = 13.661200716 x = 13.661200716 Simplifying x = 13.661200716Subproblem 2
x + -3.5 = -10.161200716 Simplifying x + -3.5 = -10.161200716 Reorder the terms: -3.5 + x = -10.161200716 Solving -3.5 + x = -10.161200716 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 = -10.161200716 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -10.161200716 + 3.5 x = -10.161200716 + 3.5 Combine like terms: -10.161200716 + 3.5 = -6.661200716 x = -6.661200716 Simplifying x = -6.661200716Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.661200716, -6.661200716}
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