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Simplifying x2 + 12x + -390 = 0 Reorder the terms: -390 + 12x + x2 = 0 Solving -390 + 12x + 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 + 12x + 390 + x2 = 0 + 390 Reorder the terms: -390 + 390 + 12x + x2 = 0 + 390 Combine like terms: -390 + 390 = 0 0 + 12x + x2 = 0 + 390 12x + x2 = 0 + 390 Combine like terms: 0 + 390 = 390 12x + x2 = 390 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 390 + 36 Reorder the terms: 36 + 12x + x2 = 390 + 36 Combine like terms: 390 + 36 = 426 36 + 12x + x2 = 426 Factor a perfect square on the left side: (x + 6)(x + 6) = 426 Calculate the square root of the right side: 20.639767441 Break this problem into two subproblems by setting (x + 6) equal to 20.639767441 and -20.639767441.Subproblem 1
x + 6 = 20.639767441 Simplifying x + 6 = 20.639767441 Reorder the terms: 6 + x = 20.639767441 Solving 6 + x = 20.639767441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 20.639767441 + -6 Combine like terms: 6 + -6 = 0 0 + x = 20.639767441 + -6 x = 20.639767441 + -6 Combine like terms: 20.639767441 + -6 = 14.639767441 x = 14.639767441 Simplifying x = 14.639767441Subproblem 2
x + 6 = -20.639767441 Simplifying x + 6 = -20.639767441 Reorder the terms: 6 + x = -20.639767441 Solving 6 + x = -20.639767441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -20.639767441 + -6 Combine like terms: 6 + -6 = 0 0 + x = -20.639767441 + -6 x = -20.639767441 + -6 Combine like terms: -20.639767441 + -6 = -26.639767441 x = -26.639767441 Simplifying x = -26.639767441Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.639767441, -26.639767441}
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