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Simplifying 6x2 + 2x + -310 = 0 Reorder the terms: -310 + 2x + 6x2 = 0 Solving -310 + 2x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-155 + x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-155 + x + 3x2)' equal to zero and attempt to solve: Simplifying -155 + x + 3x2 = 0 Solving -155 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -51.66666667 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '51.66666667' to each side of the equation. -51.66666667 + 0.3333333333x + 51.66666667 + x2 = 0 + 51.66666667 Reorder the terms: -51.66666667 + 51.66666667 + 0.3333333333x + x2 = 0 + 51.66666667 Combine like terms: -51.66666667 + 51.66666667 = 0.00000000 0.00000000 + 0.3333333333x + x2 = 0 + 51.66666667 0.3333333333x + x2 = 0 + 51.66666667 Combine like terms: 0 + 51.66666667 = 51.66666667 0.3333333333x + x2 = 51.66666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 51.66666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 51.66666667 + 0.25 Combine like terms: 51.66666667 + 0.25 = 51.91666667 0.25 + 0.3333333333x + x2 = 51.91666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 51.91666667 Calculate the square root of the right side: 7.205322107 Break this problem into two subproblems by setting (x + 0.5) equal to 7.205322107 and -7.205322107.Subproblem 1
x + 0.5 = 7.205322107 Simplifying x + 0.5 = 7.205322107 Reorder the terms: 0.5 + x = 7.205322107 Solving 0.5 + x = 7.205322107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.205322107 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.205322107 + -0.5 x = 7.205322107 + -0.5 Combine like terms: 7.205322107 + -0.5 = 6.705322107 x = 6.705322107 Simplifying x = 6.705322107Subproblem 2
x + 0.5 = -7.205322107 Simplifying x + 0.5 = -7.205322107 Reorder the terms: 0.5 + x = -7.205322107 Solving 0.5 + x = -7.205322107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.205322107 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.205322107 + -0.5 x = -7.205322107 + -0.5 Combine like terms: -7.205322107 + -0.5 = -7.705322107 x = -7.705322107 Simplifying x = -7.705322107Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.705322107, -7.705322107}Solution
x = {6.705322107, -7.705322107}
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