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Simplifying 81x2 + 16x + -4 = 0 Reorder the terms: -4 + 16x + 81x2 = 0 Solving -4 + 16x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.04938271605 + 0.1975308642x + x2 = 0 Move the constant term to the right: Add '0.04938271605' to each side of the equation. -0.04938271605 + 0.1975308642x + 0.04938271605 + x2 = 0 + 0.04938271605 Reorder the terms: -0.04938271605 + 0.04938271605 + 0.1975308642x + x2 = 0 + 0.04938271605 Combine like terms: -0.04938271605 + 0.04938271605 = 0.00000000000 0.00000000000 + 0.1975308642x + x2 = 0 + 0.04938271605 0.1975308642x + x2 = 0 + 0.04938271605 Combine like terms: 0 + 0.04938271605 = 0.04938271605 0.1975308642x + x2 = 0.04938271605 The x term is 0.1975308642x. Take half its coefficient (0.0987654321). Square it (0.009754610578) and add it to both sides. Add '0.009754610578' to each side of the equation. 0.1975308642x + 0.009754610578 + x2 = 0.04938271605 + 0.009754610578 Reorder the terms: 0.009754610578 + 0.1975308642x + x2 = 0.04938271605 + 0.009754610578 Combine like terms: 0.04938271605 + 0.009754610578 = 0.059137326628 0.009754610578 + 0.1975308642x + x2 = 0.059137326628 Factor a perfect square on the left side: (x + 0.0987654321)(x + 0.0987654321) = 0.059137326628 Calculate the square root of the right side: 0.243181674 Break this problem into two subproblems by setting (x + 0.0987654321) equal to 0.243181674 and -0.243181674.Subproblem 1
x + 0.0987654321 = 0.243181674 Simplifying x + 0.0987654321 = 0.243181674 Reorder the terms: 0.0987654321 + x = 0.243181674 Solving 0.0987654321 + x = 0.243181674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0987654321' to each side of the equation. 0.0987654321 + -0.0987654321 + x = 0.243181674 + -0.0987654321 Combine like terms: 0.0987654321 + -0.0987654321 = 0.0000000000 0.0000000000 + x = 0.243181674 + -0.0987654321 x = 0.243181674 + -0.0987654321 Combine like terms: 0.243181674 + -0.0987654321 = 0.1444162419 x = 0.1444162419 Simplifying x = 0.1444162419Subproblem 2
x + 0.0987654321 = -0.243181674 Simplifying x + 0.0987654321 = -0.243181674 Reorder the terms: 0.0987654321 + x = -0.243181674 Solving 0.0987654321 + x = -0.243181674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0987654321' to each side of the equation. 0.0987654321 + -0.0987654321 + x = -0.243181674 + -0.0987654321 Combine like terms: 0.0987654321 + -0.0987654321 = 0.0000000000 0.0000000000 + x = -0.243181674 + -0.0987654321 x = -0.243181674 + -0.0987654321 Combine like terms: -0.243181674 + -0.0987654321 = -0.3419471061 x = -0.3419471061 Simplifying x = -0.3419471061Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1444162419, -0.3419471061}
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