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Simplifying 6x2 + 10x + -81 = 0 Reorder the terms: -81 + 10x + 6x2 = 0 Solving -81 + 10x + 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'. -13.5 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 1.666666667x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 1.666666667x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 1.666666667x + x2 = 0 + 13.5 1.666666667x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 1.666666667x + x2 = 13.5 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 13.5 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 13.5 + 0.6944444447 Combine like terms: 13.5 + 0.6944444447 = 14.1944444447 0.6944444447 + 1.666666667x + x2 = 14.1944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 14.1944444447 Calculate the square root of the right side: 3.767551519 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 3.767551519 and -3.767551519.Subproblem 1
x + 0.8333333335 = 3.767551519 Simplifying x + 0.8333333335 = 3.767551519 Reorder the terms: 0.8333333335 + x = 3.767551519 Solving 0.8333333335 + x = 3.767551519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 3.767551519 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 3.767551519 + -0.8333333335 x = 3.767551519 + -0.8333333335 Combine like terms: 3.767551519 + -0.8333333335 = 2.9342181855 x = 2.9342181855 Simplifying x = 2.9342181855Subproblem 2
x + 0.8333333335 = -3.767551519 Simplifying x + 0.8333333335 = -3.767551519 Reorder the terms: 0.8333333335 + x = -3.767551519 Solving 0.8333333335 + x = -3.767551519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -3.767551519 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -3.767551519 + -0.8333333335 x = -3.767551519 + -0.8333333335 Combine like terms: -3.767551519 + -0.8333333335 = -4.6008848525 x = -4.6008848525 Simplifying x = -4.6008848525Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9342181855, -4.6008848525}
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