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Simplifying 6x2 + -17x + -40 = 0 Reorder the terms: -40 + -17x + 6x2 = 0 Solving -40 + -17x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6.666666667 + -2.833333333x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -2.833333333x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -2.833333333x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -2.833333333x + x2 = 0 + 6.666666667 -2.833333333x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -2.833333333x + x2 = 6.666666667 The x term is -2.833333333x. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333x + 2.006944445 + x2 = 6.666666667 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333x + x2 = 6.666666667 + 2.006944445 Combine like terms: 6.666666667 + 2.006944445 = 8.673611112 2.006944445 + -2.833333333x + x2 = 8.673611112 Factor a perfect square on the left side: (x + -1.416666667)(x + -1.416666667) = 8.673611112 Calculate the square root of the right side: 2.945099508 Break this problem into two subproblems by setting (x + -1.416666667) equal to 2.945099508 and -2.945099508.Subproblem 1
x + -1.416666667 = 2.945099508 Simplifying x + -1.416666667 = 2.945099508 Reorder the terms: -1.416666667 + x = 2.945099508 Solving -1.416666667 + x = 2.945099508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = 2.945099508 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = 2.945099508 + 1.416666667 x = 2.945099508 + 1.416666667 Combine like terms: 2.945099508 + 1.416666667 = 4.361766175 x = 4.361766175 Simplifying x = 4.361766175Subproblem 2
x + -1.416666667 = -2.945099508 Simplifying x + -1.416666667 = -2.945099508 Reorder the terms: -1.416666667 + x = -2.945099508 Solving -1.416666667 + x = -2.945099508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + x = -2.945099508 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + x = -2.945099508 + 1.416666667 x = -2.945099508 + 1.416666667 Combine like terms: -2.945099508 + 1.416666667 = -1.528432841 x = -1.528432841 Simplifying x = -1.528432841Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.361766175, -1.528432841}
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