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Simplifying x2 + 7x + -28 = 10 Reorder the terms: -28 + 7x + x2 = 10 Solving -28 + 7x + x2 = 10 Solving for variable 'x'. Reorder the terms: -28 + -10 + 7x + x2 = 10 + -10 Combine like terms: -28 + -10 = -38 -38 + 7x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -38 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 7x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + 7x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 7x + x2 = 0 + 38 7x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 7x + x2 = 38 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 = 38 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 38 + 12.25 Combine like terms: 38 + 12.25 = 50.25 12.25 + 7x + x2 = 50.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + 3.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + 3.5 = 7.088723439 Simplifying x + 3.5 = 7.088723439 Reorder the terms: 3.5 + x = 7.088723439 Solving 3.5 + x = 7.088723439 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 = 7.088723439 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 7.088723439 + -3.5 x = 7.088723439 + -3.5 Combine like terms: 7.088723439 + -3.5 = 3.588723439 x = 3.588723439 Simplifying x = 3.588723439Subproblem 2
x + 3.5 = -7.088723439 Simplifying x + 3.5 = -7.088723439 Reorder the terms: 3.5 + x = -7.088723439 Solving 3.5 + x = -7.088723439 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 = -7.088723439 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -7.088723439 + -3.5 x = -7.088723439 + -3.5 Combine like terms: -7.088723439 + -3.5 = -10.588723439 x = -10.588723439 Simplifying x = -10.588723439Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.588723439, -10.588723439}
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