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Simplifying 81x2 + -16 = x Reorder the terms: -16 + 81x2 = x Solving -16 + 81x2 = x Solving for variable 'x'. Reorder the terms: -16 + -1x + 81x2 = x + -1x Combine like terms: x + -1x = 0 -16 + -1x + 81x2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.1975308642 + -0.01234567901x + x2 = 0 Move the constant term to the right: Add '0.1975308642' to each side of the equation. -0.1975308642 + -0.01234567901x + 0.1975308642 + x2 = 0 + 0.1975308642 Reorder the terms: -0.1975308642 + 0.1975308642 + -0.01234567901x + x2 = 0 + 0.1975308642 Combine like terms: -0.1975308642 + 0.1975308642 = 0.0000000000 0.0000000000 + -0.01234567901x + x2 = 0 + 0.1975308642 -0.01234567901x + x2 = 0 + 0.1975308642 Combine like terms: 0 + 0.1975308642 = 0.1975308642 -0.01234567901x + x2 = 0.1975308642 The x term is -0.01234567901x. Take half its coefficient (-0.006172839505). Square it (0.00003810394755) and add it to both sides. Add '0.00003810394755' to each side of the equation. -0.01234567901x + 0.00003810394755 + x2 = 0.1975308642 + 0.00003810394755 Reorder the terms: 0.00003810394755 + -0.01234567901x + x2 = 0.1975308642 + 0.00003810394755 Combine like terms: 0.1975308642 + 0.00003810394755 = 0.19756896814755 0.00003810394755 + -0.01234567901x + x2 = 0.19756896814755 Factor a perfect square on the left side: (x + -0.006172839505)(x + -0.006172839505) = 0.19756896814755 Calculate the square root of the right side: 0.444487309 Break this problem into two subproblems by setting (x + -0.006172839505) equal to 0.444487309 and -0.444487309.Subproblem 1
x + -0.006172839505 = 0.444487309 Simplifying x + -0.006172839505 = 0.444487309 Reorder the terms: -0.006172839505 + x = 0.444487309 Solving -0.006172839505 + x = 0.444487309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006172839505' to each side of the equation. -0.006172839505 + 0.006172839505 + x = 0.444487309 + 0.006172839505 Combine like terms: -0.006172839505 + 0.006172839505 = 0.000000000000 0.000000000000 + x = 0.444487309 + 0.006172839505 x = 0.444487309 + 0.006172839505 Combine like terms: 0.444487309 + 0.006172839505 = 0.450660148505 x = 0.450660148505 Simplifying x = 0.450660148505Subproblem 2
x + -0.006172839505 = -0.444487309 Simplifying x + -0.006172839505 = -0.444487309 Reorder the terms: -0.006172839505 + x = -0.444487309 Solving -0.006172839505 + x = -0.444487309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006172839505' to each side of the equation. -0.006172839505 + 0.006172839505 + x = -0.444487309 + 0.006172839505 Combine like terms: -0.006172839505 + 0.006172839505 = 0.000000000000 0.000000000000 + x = -0.444487309 + 0.006172839505 x = -0.444487309 + 0.006172839505 Combine like terms: -0.444487309 + 0.006172839505 = -0.438314469495 x = -0.438314469495 Simplifying x = -0.438314469495Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.450660148505, -0.438314469495}
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