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Simplifying x(x + 11) = 66 Reorder the terms: x(11 + x) = 66 (11 * x + x * x) = 66 (11x + x2) = 66 Solving 11x + x2 = 66 Solving for variable 'x'. Reorder the terms: -66 + 11x + x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -66 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 11x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + 11x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 11x + x2 = 0 + 66 11x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 11x + x2 = 66 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 66 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 66 + 30.25 Combine like terms: 66 + 30.25 = 96.25 30.25 + 11x + x2 = 96.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 96.25 Calculate the square root of the right side: 9.810708435 Break this problem into two subproblems by setting (x + 5.5) equal to 9.810708435 and -9.810708435.Subproblem 1
x + 5.5 = 9.810708435 Simplifying x + 5.5 = 9.810708435 Reorder the terms: 5.5 + x = 9.810708435 Solving 5.5 + x = 9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 9.810708435 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 9.810708435 + -5.5 x = 9.810708435 + -5.5 Combine like terms: 9.810708435 + -5.5 = 4.310708435 x = 4.310708435 Simplifying x = 4.310708435Subproblem 2
x + 5.5 = -9.810708435 Simplifying x + 5.5 = -9.810708435 Reorder the terms: 5.5 + x = -9.810708435 Solving 5.5 + x = -9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -9.810708435 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -9.810708435 + -5.5 x = -9.810708435 + -5.5 Combine like terms: -9.810708435 + -5.5 = -15.310708435 x = -15.310708435 Simplifying x = -15.310708435Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.310708435, -15.310708435}
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