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Simplifying 6x2 + -30x + -7 = 0 Reorder the terms: -7 + -30x + 6x2 = 0 Solving -7 + -30x + 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'. -1.166666667 + -5x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -5x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -5x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -5x + x2 = 0 + 1.166666667 -5x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -5x + x2 = 1.166666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 1.166666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1.166666667 + 6.25 Combine like terms: 1.166666667 + 6.25 = 7.416666667 6.25 + -5x + x2 = 7.416666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7.416666667 Calculate the square root of the right side: 2.723355773 Break this problem into two subproblems by setting (x + -2.5) equal to 2.723355773 and -2.723355773.Subproblem 1
x + -2.5 = 2.723355773 Simplifying x + -2.5 = 2.723355773 Reorder the terms: -2.5 + x = 2.723355773 Solving -2.5 + x = 2.723355773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.723355773 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.723355773 + 2.5 x = 2.723355773 + 2.5 Combine like terms: 2.723355773 + 2.5 = 5.223355773 x = 5.223355773 Simplifying x = 5.223355773Subproblem 2
x + -2.5 = -2.723355773 Simplifying x + -2.5 = -2.723355773 Reorder the terms: -2.5 + x = -2.723355773 Solving -2.5 + x = -2.723355773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.723355773 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.723355773 + 2.5 x = -2.723355773 + 2.5 Combine like terms: -2.723355773 + 2.5 = -0.223355773 x = -0.223355773 Simplifying x = -0.223355773Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.223355773, -0.223355773}
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