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Simplifying 6x2 + 14x + -3 = 0 Reorder the terms: -3 + 14x + 6x2 = 0 Solving -3 + 14x + 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'. -0.5 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 2.333333333x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 2.333333333x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 2.333333333x + x2 = 0 + 0.5 2.333333333x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 2.333333333x + x2 = 0.5 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 0.5 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 0.5 + 1.361111112 Combine like terms: 0.5 + 1.361111112 = 1.861111112 1.361111112 + 2.333333333x + x2 = 1.861111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 1.861111112 Calculate the square root of the right side: 1.364225462 Break this problem into two subproblems by setting (x + 1.166666667) equal to 1.364225462 and -1.364225462.Subproblem 1
x + 1.166666667 = 1.364225462 Simplifying x + 1.166666667 = 1.364225462 Reorder the terms: 1.166666667 + x = 1.364225462 Solving 1.166666667 + x = 1.364225462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 1.364225462 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 1.364225462 + -1.166666667 x = 1.364225462 + -1.166666667 Combine like terms: 1.364225462 + -1.166666667 = 0.197558795 x = 0.197558795 Simplifying x = 0.197558795Subproblem 2
x + 1.166666667 = -1.364225462 Simplifying x + 1.166666667 = -1.364225462 Reorder the terms: 1.166666667 + x = -1.364225462 Solving 1.166666667 + x = -1.364225462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -1.364225462 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -1.364225462 + -1.166666667 x = -1.364225462 + -1.166666667 Combine like terms: -1.364225462 + -1.166666667 = -2.530892129 x = -2.530892129 Simplifying x = -2.530892129Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.197558795, -2.530892129}
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