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Simplifying x2 + -12x + -1620 = 0 Reorder the terms: -1620 + -12x + x2 = 0 Solving -1620 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1620' to each side of the equation. -1620 + -12x + 1620 + x2 = 0 + 1620 Reorder the terms: -1620 + 1620 + -12x + x2 = 0 + 1620 Combine like terms: -1620 + 1620 = 0 0 + -12x + x2 = 0 + 1620 -12x + x2 = 0 + 1620 Combine like terms: 0 + 1620 = 1620 -12x + x2 = 1620 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 = 1620 + 36 Reorder the terms: 36 + -12x + x2 = 1620 + 36 Combine like terms: 1620 + 36 = 1656 36 + -12x + x2 = 1656 Factor a perfect square on the left side: (x + -6)(x + -6) = 1656 Calculate the square root of the right side: 40.693979899 Break this problem into two subproblems by setting (x + -6) equal to 40.693979899 and -40.693979899.Subproblem 1
x + -6 = 40.693979899 Simplifying x + -6 = 40.693979899 Reorder the terms: -6 + x = 40.693979899 Solving -6 + x = 40.693979899 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 = 40.693979899 + 6 Combine like terms: -6 + 6 = 0 0 + x = 40.693979899 + 6 x = 40.693979899 + 6 Combine like terms: 40.693979899 + 6 = 46.693979899 x = 46.693979899 Simplifying x = 46.693979899Subproblem 2
x + -6 = -40.693979899 Simplifying x + -6 = -40.693979899 Reorder the terms: -6 + x = -40.693979899 Solving -6 + x = -40.693979899 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 = -40.693979899 + 6 Combine like terms: -6 + 6 = 0 0 + x = -40.693979899 + 6 x = -40.693979899 + 6 Combine like terms: -40.693979899 + 6 = -34.693979899 x = -34.693979899 Simplifying x = -34.693979899Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.693979899, -34.693979899}
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