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Simplifying x2 + 10x + 3 = 21 Reorder the terms: 3 + 10x + x2 = 21 Solving 3 + 10x + x2 = 21 Solving for variable 'x'. Reorder the terms: 3 + -21 + 10x + x2 = 21 + -21 Combine like terms: 3 + -21 = -18 -18 + 10x + x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -18 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 10x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 10x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 10x + x2 = 0 + 18 10x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 10x + x2 = 18 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 = 18 + 25 Reorder the terms: 25 + 10x + x2 = 18 + 25 Combine like terms: 18 + 25 = 43 25 + 10x + x2 = 43 Factor a perfect square on the left side: (x + 5)(x + 5) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (x + 5) equal to 6.557438524 and -6.557438524.Subproblem 1
x + 5 = 6.557438524 Simplifying x + 5 = 6.557438524 Reorder the terms: 5 + x = 6.557438524 Solving 5 + x = 6.557438524 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 = 6.557438524 + -5 Combine like terms: 5 + -5 = 0 0 + x = 6.557438524 + -5 x = 6.557438524 + -5 Combine like terms: 6.557438524 + -5 = 1.557438524 x = 1.557438524 Simplifying x = 1.557438524Subproblem 2
x + 5 = -6.557438524 Simplifying x + 5 = -6.557438524 Reorder the terms: 5 + x = -6.557438524 Solving 5 + x = -6.557438524 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 = -6.557438524 + -5 Combine like terms: 5 + -5 = 0 0 + x = -6.557438524 + -5 x = -6.557438524 + -5 Combine like terms: -6.557438524 + -5 = -11.557438524 x = -11.557438524 Simplifying x = -11.557438524Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.557438524, -11.557438524}
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