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Simplifying 6x2 + 42x + 35 = 0 Reorder the terms: 35 + 42x + 6x2 = 0 Solving 35 + 42x + 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'. 5.833333333 + 7x + x2 = 0 Move the constant term to the right: Add '-5.833333333' to each side of the equation. 5.833333333 + 7x + -5.833333333 + x2 = 0 + -5.833333333 Reorder the terms: 5.833333333 + -5.833333333 + 7x + x2 = 0 + -5.833333333 Combine like terms: 5.833333333 + -5.833333333 = 0.000000000 0.000000000 + 7x + x2 = 0 + -5.833333333 7x + x2 = 0 + -5.833333333 Combine like terms: 0 + -5.833333333 = -5.833333333 7x + x2 = -5.833333333 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -5.833333333 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -5.833333333 + 12.25 Combine like terms: -5.833333333 + 12.25 = 6.416666667 12.25 + 7x + x2 = 6.416666667 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 6.416666667 Calculate the square root of the right side: 2.533114026 Break this problem into two subproblems by setting (x + 3.5) equal to 2.533114026 and -2.533114026.Subproblem 1
x + 3.5 = 2.533114026 Simplifying x + 3.5 = 2.533114026 Reorder the terms: 3.5 + x = 2.533114026 Solving 3.5 + x = 2.533114026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.533114026 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.533114026 + -3.5 x = 2.533114026 + -3.5 Combine like terms: 2.533114026 + -3.5 = -0.966885974 x = -0.966885974 Simplifying x = -0.966885974Subproblem 2
x + 3.5 = -2.533114026 Simplifying x + 3.5 = -2.533114026 Reorder the terms: 3.5 + x = -2.533114026 Solving 3.5 + x = -2.533114026 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.533114026 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.533114026 + -3.5 x = -2.533114026 + -3.5 Combine like terms: -2.533114026 + -3.5 = -6.033114026 x = -6.033114026 Simplifying x = -6.033114026Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.966885974, -6.033114026}
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