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Simplifying x2 + 10x = 19 Reorder the terms: 10x + x2 = 19 Solving 10x + x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + 10x + x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 10x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 10x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 10x + x2 = 0 + 19 10x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 10x + x2 = 19 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 19 + 25 Reorder the terms: 25 + 10x + x2 = 19 + 25 Combine like terms: 19 + 25 = 44 25 + 10x + x2 = 44 Factor a perfect square on the left side: (x + 5)(x + 5) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + 5) equal to 6.633249581 and -6.633249581.Subproblem 1
x + 5 = 6.633249581 Simplifying x + 5 = 6.633249581 Reorder the terms: 5 + x = 6.633249581 Solving 5 + x = 6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 6.633249581 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.633249581 + -5 x = 6.633249581 + -5 Combine like terms: 6.633249581 + -5 = 1.633249581 x = 1.633249581 Simplifying x = 1.633249581Subproblem 2
x + 5 = -6.633249581 Simplifying x + 5 = -6.633249581 Reorder the terms: 5 + x = -6.633249581 Solving 5 + x = -6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -6.633249581 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.633249581 + -5 x = -6.633249581 + -5 Combine like terms: -6.633249581 + -5 = -11.633249581 x = -11.633249581 Simplifying x = -11.633249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.633249581, -11.633249581}
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