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Simplifying x + 6 + 4x2 = 81 Reorder the terms: 6 + x + 4x2 = 81 Solving 6 + x + 4x2 = 81 Solving for variable 'x'. Reorder the terms: 6 + -81 + x + 4x2 = 81 + -81 Combine like terms: 6 + -81 = -75 -75 + x + 4x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -75 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18.75 + 0.25x + x2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + 0.25x + 18.75 + x2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + 0.25x + x2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + 0.25x + x2 = 0 + 18.75 0.25x + x2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 0.25x + x2 = 18.75 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. 0.25x + 0.25 + x2 = 18.75 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 18.75 + 0.25 Combine like terms: 18.75 + 0.25 = 19 0.25 + 0.25x + x2 = 19 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 0.5) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 0.5 = 4.358898944 Simplifying x + 0.5 = 4.358898944 Reorder the terms: 0.5 + x = 4.358898944 Solving 0.5 + x = 4.358898944 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 = 4.358898944 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.358898944 + -0.5 x = 4.358898944 + -0.5 Combine like terms: 4.358898944 + -0.5 = 3.858898944 x = 3.858898944 Simplifying x = 3.858898944Subproblem 2
x + 0.5 = -4.358898944 Simplifying x + 0.5 = -4.358898944 Reorder the terms: 0.5 + x = -4.358898944 Solving 0.5 + x = -4.358898944 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 = -4.358898944 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.358898944 + -0.5 x = -4.358898944 + -0.5 Combine like terms: -4.358898944 + -0.5 = -4.858898944 x = -4.858898944 Simplifying x = -4.858898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.858898944, -4.858898944}
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