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Simplifying x2 + 4x + -342 = 0 Reorder the terms: -342 + 4x + x2 = 0 Solving -342 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '342' to each side of the equation. -342 + 4x + 342 + x2 = 0 + 342 Reorder the terms: -342 + 342 + 4x + x2 = 0 + 342 Combine like terms: -342 + 342 = 0 0 + 4x + x2 = 0 + 342 4x + x2 = 0 + 342 Combine like terms: 0 + 342 = 342 4x + x2 = 342 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 342 + 4 Reorder the terms: 4 + 4x + x2 = 342 + 4 Combine like terms: 342 + 4 = 346 4 + 4x + x2 = 346 Factor a perfect square on the left side: (x + 2)(x + 2) = 346 Calculate the square root of the right side: 18.601075238 Break this problem into two subproblems by setting (x + 2) equal to 18.601075238 and -18.601075238.Subproblem 1
x + 2 = 18.601075238 Simplifying x + 2 = 18.601075238 Reorder the terms: 2 + x = 18.601075238 Solving 2 + x = 18.601075238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 18.601075238 + -2 Combine like terms: 2 + -2 = 0 0 + x = 18.601075238 + -2 x = 18.601075238 + -2 Combine like terms: 18.601075238 + -2 = 16.601075238 x = 16.601075238 Simplifying x = 16.601075238Subproblem 2
x + 2 = -18.601075238 Simplifying x + 2 = -18.601075238 Reorder the terms: 2 + x = -18.601075238 Solving 2 + x = -18.601075238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -18.601075238 + -2 Combine like terms: 2 + -2 = 0 0 + x = -18.601075238 + -2 x = -18.601075238 + -2 Combine like terms: -18.601075238 + -2 = -20.601075238 x = -20.601075238 Simplifying x = -20.601075238Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.601075238, -20.601075238}
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