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Simplifying (x + 5) * 2 + (x + -2) * 2 + (x + -7)(x + 7) = 11x + 30 Reorder the terms: (5 + x) * 2 + (x + -2) * 2 + (x + -7)(x + 7) = 11x + 30 Reorder the terms for easier multiplication: 2(5 + x) + (x + -2) * 2 + (x + -7)(x + 7) = 11x + 30 (5 * 2 + x * 2) + (x + -2) * 2 + (x + -7)(x + 7) = 11x + 30 (10 + 2x) + (x + -2) * 2 + (x + -7)(x + 7) = 11x + 30 Reorder the terms: 10 + 2x + (-2 + x) * 2 + (x + -7)(x + 7) = 11x + 30 Reorder the terms for easier multiplication: 10 + 2x + 2(-2 + x) + (x + -7)(x + 7) = 11x + 30 10 + 2x + (-2 * 2 + x * 2) + (x + -7)(x + 7) = 11x + 30 10 + 2x + (-4 + 2x) + (x + -7)(x + 7) = 11x + 30 Reorder the terms: 10 + 2x + -4 + 2x + (-7 + x)(x + 7) = 11x + 30 Reorder the terms: 10 + 2x + -4 + 2x + (-7 + x)(7 + x) = 11x + 30 Multiply (-7 + x) * (7 + x) 10 + 2x + -4 + 2x + (-7(7 + x) + x(7 + x)) = 11x + 30 10 + 2x + -4 + 2x + ((7 * -7 + x * -7) + x(7 + x)) = 11x + 30 10 + 2x + -4 + 2x + ((-49 + -7x) + x(7 + x)) = 11x + 30 10 + 2x + -4 + 2x + (-49 + -7x + (7 * x + x * x)) = 11x + 30 10 + 2x + -4 + 2x + (-49 + -7x + (7x + x2)) = 11x + 30 Combine like terms: -7x + 7x = 0 10 + 2x + -4 + 2x + (-49 + 0 + x2) = 11x + 30 10 + 2x + -4 + 2x + (-49 + x2) = 11x + 30 Reorder the terms: 10 + -4 + -49 + 2x + 2x + x2 = 11x + 30 Combine like terms: 10 + -4 = 6 6 + -49 + 2x + 2x + x2 = 11x + 30 Combine like terms: 6 + -49 = -43 -43 + 2x + 2x + x2 = 11x + 30 Combine like terms: 2x + 2x = 4x -43 + 4x + x2 = 11x + 30 Reorder the terms: -43 + 4x + x2 = 30 + 11x Solving -43 + 4x + x2 = 30 + 11x Solving for variable 'x'. Reorder the terms: -43 + -30 + 4x + -11x + x2 = 30 + 11x + -30 + -11x Combine like terms: -43 + -30 = -73 -73 + 4x + -11x + x2 = 30 + 11x + -30 + -11x Combine like terms: 4x + -11x = -7x -73 + -7x + x2 = 30 + 11x + -30 + -11x Reorder the terms: -73 + -7x + x2 = 30 + -30 + 11x + -11x Combine like terms: 30 + -30 = 0 -73 + -7x + x2 = 0 + 11x + -11x -73 + -7x + x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -73 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + -7x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + -7x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + -7x + x2 = 0 + 73 -7x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 -7x + x2 = 73 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 = 73 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 73 + 12.25 Combine like terms: 73 + 12.25 = 85.25 12.25 + -7x + x2 = 85.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 85.25 Calculate the square root of the right side: 9.233092656 Break this problem into two subproblems by setting (x + -3.5) equal to 9.233092656 and -9.233092656.Subproblem 1
x + -3.5 = 9.233092656 Simplifying x + -3.5 = 9.233092656 Reorder the terms: -3.5 + x = 9.233092656 Solving -3.5 + x = 9.233092656 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 = 9.233092656 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 9.233092656 + 3.5 x = 9.233092656 + 3.5 Combine like terms: 9.233092656 + 3.5 = 12.733092656 x = 12.733092656 Simplifying x = 12.733092656Subproblem 2
x + -3.5 = -9.233092656 Simplifying x + -3.5 = -9.233092656 Reorder the terms: -3.5 + x = -9.233092656 Solving -3.5 + x = -9.233092656 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 = -9.233092656 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -9.233092656 + 3.5 x = -9.233092656 + 3.5 Combine like terms: -9.233092656 + 3.5 = -5.733092656 x = -5.733092656 Simplifying x = -5.733092656Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.733092656, -5.733092656}
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