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Simplifying X2 + -47X + -42 = 0 Reorder the terms: -42 + -47X + X2 = 0 Solving -42 + -47X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -47X + 42 + X2 = 0 + 42 Reorder the terms: -42 + 42 + -47X + X2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -47X + X2 = 0 + 42 -47X + X2 = 0 + 42 Combine like terms: 0 + 42 = 42 -47X + X2 = 42 The X term is -47X. Take half its coefficient (-23.5). Square it (552.25) and add it to both sides. Add '552.25' to each side of the equation. -47X + 552.25 + X2 = 42 + 552.25 Reorder the terms: 552.25 + -47X + X2 = 42 + 552.25 Combine like terms: 42 + 552.25 = 594.25 552.25 + -47X + X2 = 594.25 Factor a perfect square on the left side: (X + -23.5)(X + -23.5) = 594.25 Calculate the square root of the right side: 24.377243486 Break this problem into two subproblems by setting (X + -23.5) equal to 24.377243486 and -24.377243486.Subproblem 1
X + -23.5 = 24.377243486 Simplifying X + -23.5 = 24.377243486 Reorder the terms: -23.5 + X = 24.377243486 Solving -23.5 + X = 24.377243486 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + X = 24.377243486 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + X = 24.377243486 + 23.5 X = 24.377243486 + 23.5 Combine like terms: 24.377243486 + 23.5 = 47.877243486 X = 47.877243486 Simplifying X = 47.877243486Subproblem 2
X + -23.5 = -24.377243486 Simplifying X + -23.5 = -24.377243486 Reorder the terms: -23.5 + X = -24.377243486 Solving -23.5 + X = -24.377243486 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '23.5' to each side of the equation. -23.5 + 23.5 + X = -24.377243486 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + X = -24.377243486 + 23.5 X = -24.377243486 + 23.5 Combine like terms: -24.377243486 + 23.5 = -0.877243486 X = -0.877243486 Simplifying X = -0.877243486Solution
The solution to the problem is based on the solutions from the subproblems. X = {47.877243486, -0.877243486}
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