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Simplifying x2 + 10x + -144 = 3 Reorder the terms: -144 + 10x + x2 = 3 Solving -144 + 10x + x2 = 3 Solving for variable 'x'. Reorder the terms: -144 + -3 + 10x + x2 = 3 + -3 Combine like terms: -144 + -3 = -147 -147 + 10x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -147 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '147' to each side of the equation. -147 + 10x + 147 + x2 = 0 + 147 Reorder the terms: -147 + 147 + 10x + x2 = 0 + 147 Combine like terms: -147 + 147 = 0 0 + 10x + x2 = 0 + 147 10x + x2 = 0 + 147 Combine like terms: 0 + 147 = 147 10x + x2 = 147 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 = 147 + 25 Reorder the terms: 25 + 10x + x2 = 147 + 25 Combine like terms: 147 + 25 = 172 25 + 10x + x2 = 172 Factor a perfect square on the left side: (x + 5)(x + 5) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (x + 5) equal to 13.114877049 and -13.114877049.Subproblem 1
x + 5 = 13.114877049 Simplifying x + 5 = 13.114877049 Reorder the terms: 5 + x = 13.114877049 Solving 5 + x = 13.114877049 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 = 13.114877049 + -5 Combine like terms: 5 + -5 = 0 0 + x = 13.114877049 + -5 x = 13.114877049 + -5 Combine like terms: 13.114877049 + -5 = 8.114877049 x = 8.114877049 Simplifying x = 8.114877049Subproblem 2
x + 5 = -13.114877049 Simplifying x + 5 = -13.114877049 Reorder the terms: 5 + x = -13.114877049 Solving 5 + x = -13.114877049 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 = -13.114877049 + -5 Combine like terms: 5 + -5 = 0 0 + x = -13.114877049 + -5 x = -13.114877049 + -5 Combine like terms: -13.114877049 + -5 = -18.114877049 x = -18.114877049 Simplifying x = -18.114877049Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.114877049, -18.114877049}
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