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Simplifying x2 + 10x + 21 = 144 Reorder the terms: 21 + 10x + x2 = 144 Solving 21 + 10x + x2 = 144 Solving for variable 'x'. Reorder the terms: 21 + -144 + 10x + x2 = 144 + -144 Combine like terms: 21 + -144 = -123 -123 + 10x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -123 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '123' to each side of the equation. -123 + 10x + 123 + x2 = 0 + 123 Reorder the terms: -123 + 123 + 10x + x2 = 0 + 123 Combine like terms: -123 + 123 = 0 0 + 10x + x2 = 0 + 123 10x + x2 = 0 + 123 Combine like terms: 0 + 123 = 123 10x + x2 = 123 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 = 123 + 25 Reorder the terms: 25 + 10x + x2 = 123 + 25 Combine like terms: 123 + 25 = 148 25 + 10x + x2 = 148 Factor a perfect square on the left side: (x + 5)(x + 5) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (x + 5) equal to 12.165525061 and -12.165525061.Subproblem 1
x + 5 = 12.165525061 Simplifying x + 5 = 12.165525061 Reorder the terms: 5 + x = 12.165525061 Solving 5 + x = 12.165525061 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 = 12.165525061 + -5 Combine like terms: 5 + -5 = 0 0 + x = 12.165525061 + -5 x = 12.165525061 + -5 Combine like terms: 12.165525061 + -5 = 7.165525061 x = 7.165525061 Simplifying x = 7.165525061Subproblem 2
x + 5 = -12.165525061 Simplifying x + 5 = -12.165525061 Reorder the terms: 5 + x = -12.165525061 Solving 5 + x = -12.165525061 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 = -12.165525061 + -5 Combine like terms: 5 + -5 = 0 0 + x = -12.165525061 + -5 x = -12.165525061 + -5 Combine like terms: -12.165525061 + -5 = -17.165525061 x = -17.165525061 Simplifying x = -17.165525061Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.165525061, -17.165525061}
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