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Simplifying x2 + 4x + -390 = 0 Reorder the terms: -390 + 4x + x2 = 0 Solving -390 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '390' to each side of the equation. -390 + 4x + 390 + x2 = 0 + 390 Reorder the terms: -390 + 390 + 4x + x2 = 0 + 390 Combine like terms: -390 + 390 = 0 0 + 4x + x2 = 0 + 390 4x + x2 = 0 + 390 Combine like terms: 0 + 390 = 390 4x + x2 = 390 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 = 390 + 4 Reorder the terms: 4 + 4x + x2 = 390 + 4 Combine like terms: 390 + 4 = 394 4 + 4x + x2 = 394 Factor a perfect square on the left side: (x + 2)(x + 2) = 394 Calculate the square root of the right side: 19.849433241 Break this problem into two subproblems by setting (x + 2) equal to 19.849433241 and -19.849433241.Subproblem 1
x + 2 = 19.849433241 Simplifying x + 2 = 19.849433241 Reorder the terms: 2 + x = 19.849433241 Solving 2 + x = 19.849433241 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 = 19.849433241 + -2 Combine like terms: 2 + -2 = 0 0 + x = 19.849433241 + -2 x = 19.849433241 + -2 Combine like terms: 19.849433241 + -2 = 17.849433241 x = 17.849433241 Simplifying x = 17.849433241Subproblem 2
x + 2 = -19.849433241 Simplifying x + 2 = -19.849433241 Reorder the terms: 2 + x = -19.849433241 Solving 2 + x = -19.849433241 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 = -19.849433241 + -2 Combine like terms: 2 + -2 = 0 0 + x = -19.849433241 + -2 x = -19.849433241 + -2 Combine like terms: -19.849433241 + -2 = -21.849433241 x = -21.849433241 Simplifying x = -21.849433241Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.849433241, -21.849433241}
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