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Simplifying 6x * 6x + 11x + -72 = 0 Reorder the terms for easier multiplication: 6 * 6x * x + 11x + -72 = 0 Multiply 6 * 6 36x * x + 11x + -72 = 0 Multiply x * x 36x2 + 11x + -72 = 0 Reorder the terms: -72 + 11x + 36x2 = 0 Solving -72 + 11x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -2 + 0.3055555556x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.3055555556x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.3055555556x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.3055555556x + x2 = 0 + 2 0.3055555556x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.3055555556x + x2 = 2 The x term is 0.3055555556x. Take half its coefficient (0.1527777778). Square it (0.02334104939) and add it to both sides. Add '0.02334104939' to each side of the equation. 0.3055555556x + 0.02334104939 + x2 = 2 + 0.02334104939 Reorder the terms: 0.02334104939 + 0.3055555556x + x2 = 2 + 0.02334104939 Combine like terms: 2 + 0.02334104939 = 2.02334104939 0.02334104939 + 0.3055555556x + x2 = 2.02334104939 Factor a perfect square on the left side: (x + 0.1527777778)(x + 0.1527777778) = 2.02334104939 Calculate the square root of the right side: 1.422441932 Break this problem into two subproblems by setting (x + 0.1527777778) equal to 1.422441932 and -1.422441932.Subproblem 1
x + 0.1527777778 = 1.422441932 Simplifying x + 0.1527777778 = 1.422441932 Reorder the terms: 0.1527777778 + x = 1.422441932 Solving 0.1527777778 + x = 1.422441932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1527777778' to each side of the equation. 0.1527777778 + -0.1527777778 + x = 1.422441932 + -0.1527777778 Combine like terms: 0.1527777778 + -0.1527777778 = 0.0000000000 0.0000000000 + x = 1.422441932 + -0.1527777778 x = 1.422441932 + -0.1527777778 Combine like terms: 1.422441932 + -0.1527777778 = 1.2696641542 x = 1.2696641542 Simplifying x = 1.2696641542Subproblem 2
x + 0.1527777778 = -1.422441932 Simplifying x + 0.1527777778 = -1.422441932 Reorder the terms: 0.1527777778 + x = -1.422441932 Solving 0.1527777778 + x = -1.422441932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1527777778' to each side of the equation. 0.1527777778 + -0.1527777778 + x = -1.422441932 + -0.1527777778 Combine like terms: 0.1527777778 + -0.1527777778 = 0.0000000000 0.0000000000 + x = -1.422441932 + -0.1527777778 x = -1.422441932 + -0.1527777778 Combine like terms: -1.422441932 + -0.1527777778 = -1.5752197098 x = -1.5752197098 Simplifying x = -1.5752197098Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2696641542, -1.5752197098}
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