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Simplifying (x2 + 3x + -1) + (7x + -4) = 0 Reorder the terms: (-1 + 3x + x2) + (7x + -4) = 0 Remove parenthesis around (-1 + 3x + x2) -1 + 3x + x2 + (7x + -4) = 0 Reorder the terms: -1 + 3x + x2 + (-4 + 7x) = 0 Remove parenthesis around (-4 + 7x) -1 + 3x + x2 + -4 + 7x = 0 Reorder the terms: -1 + -4 + 3x + 7x + x2 = 0 Combine like terms: -1 + -4 = -5 -5 + 3x + 7x + x2 = 0 Combine like terms: 3x + 7x = 10x -5 + 10x + x2 = 0 Solving -5 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 10x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 10x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 10x + x2 = 0 + 5 10x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 10x + x2 = 5 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 = 5 + 25 Reorder the terms: 25 + 10x + x2 = 5 + 25 Combine like terms: 5 + 25 = 30 25 + 10x + x2 = 30 Factor a perfect square on the left side: (x + 5)(x + 5) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (x + 5) equal to 5.477225575 and -5.477225575.Subproblem 1
x + 5 = 5.477225575 Simplifying x + 5 = 5.477225575 Reorder the terms: 5 + x = 5.477225575 Solving 5 + x = 5.477225575 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 = 5.477225575 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.477225575 + -5 x = 5.477225575 + -5 Combine like terms: 5.477225575 + -5 = 0.477225575 x = 0.477225575 Simplifying x = 0.477225575Subproblem 2
x + 5 = -5.477225575 Simplifying x + 5 = -5.477225575 Reorder the terms: 5 + x = -5.477225575 Solving 5 + x = -5.477225575 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 = -5.477225575 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.477225575 + -5 x = -5.477225575 + -5 Combine like terms: -5.477225575 + -5 = -10.477225575 x = -10.477225575 Simplifying x = -10.477225575Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.477225575, -10.477225575}
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