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Simplifying 6x2 + 35x + -69 = 0 Reorder the terms: -69 + 35x + 6x2 = 0 Solving -69 + 35x + 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'. -11.5 + 5.833333333x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + 5.833333333x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + 5.833333333x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + 5.833333333x + x2 = 0 + 11.5 5.833333333x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 5.833333333x + x2 = 11.5 The x term is 5.833333333x. Take half its coefficient (2.916666667). Square it (8.506944446) and add it to both sides. Add '8.506944446' to each side of the equation. 5.833333333x + 8.506944446 + x2 = 11.5 + 8.506944446 Reorder the terms: 8.506944446 + 5.833333333x + x2 = 11.5 + 8.506944446 Combine like terms: 11.5 + 8.506944446 = 20.006944446 8.506944446 + 5.833333333x + x2 = 20.006944446 Factor a perfect square on the left side: (x + 2.916666667)(x + 2.916666667) = 20.006944446 Calculate the square root of the right side: 4.4729123 Break this problem into two subproblems by setting (x + 2.916666667) equal to 4.4729123 and -4.4729123.Subproblem 1
x + 2.916666667 = 4.4729123 Simplifying x + 2.916666667 = 4.4729123 Reorder the terms: 2.916666667 + x = 4.4729123 Solving 2.916666667 + x = 4.4729123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.916666667' to each side of the equation. 2.916666667 + -2.916666667 + x = 4.4729123 + -2.916666667 Combine like terms: 2.916666667 + -2.916666667 = 0.000000000 0.000000000 + x = 4.4729123 + -2.916666667 x = 4.4729123 + -2.916666667 Combine like terms: 4.4729123 + -2.916666667 = 1.556245633 x = 1.556245633 Simplifying x = 1.556245633Subproblem 2
x + 2.916666667 = -4.4729123 Simplifying x + 2.916666667 = -4.4729123 Reorder the terms: 2.916666667 + x = -4.4729123 Solving 2.916666667 + x = -4.4729123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.916666667' to each side of the equation. 2.916666667 + -2.916666667 + x = -4.4729123 + -2.916666667 Combine like terms: 2.916666667 + -2.916666667 = 0.000000000 0.000000000 + x = -4.4729123 + -2.916666667 x = -4.4729123 + -2.916666667 Combine like terms: -4.4729123 + -2.916666667 = -7.389578967 x = -7.389578967 Simplifying x = -7.389578967Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.556245633, -7.389578967}
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