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Simplifying 21x2 + 116x + 80 = 0 Reorder the terms: 80 + 116x + 21x2 = 0 Solving 80 + 116x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 3.80952381 + 5.523809524x + x2 = 0 Move the constant term to the right: Add '-3.80952381' to each side of the equation. 3.80952381 + 5.523809524x + -3.80952381 + x2 = 0 + -3.80952381 Reorder the terms: 3.80952381 + -3.80952381 + 5.523809524x + x2 = 0 + -3.80952381 Combine like terms: 3.80952381 + -3.80952381 = 0.00000000 0.00000000 + 5.523809524x + x2 = 0 + -3.80952381 5.523809524x + x2 = 0 + -3.80952381 Combine like terms: 0 + -3.80952381 = -3.80952381 5.523809524x + x2 = -3.80952381 The x term is 5.523809524x. Take half its coefficient (2.761904762). Square it (7.628117914) and add it to both sides. Add '7.628117914' to each side of the equation. 5.523809524x + 7.628117914 + x2 = -3.80952381 + 7.628117914 Reorder the terms: 7.628117914 + 5.523809524x + x2 = -3.80952381 + 7.628117914 Combine like terms: -3.80952381 + 7.628117914 = 3.818594104 7.628117914 + 5.523809524x + x2 = 3.818594104 Factor a perfect square on the left side: (x + 2.761904762)(x + 2.761904762) = 3.818594104 Calculate the square root of the right side: 1.954122336 Break this problem into two subproblems by setting (x + 2.761904762) equal to 1.954122336 and -1.954122336.Subproblem 1
x + 2.761904762 = 1.954122336 Simplifying x + 2.761904762 = 1.954122336 Reorder the terms: 2.761904762 + x = 1.954122336 Solving 2.761904762 + x = 1.954122336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.761904762' to each side of the equation. 2.761904762 + -2.761904762 + x = 1.954122336 + -2.761904762 Combine like terms: 2.761904762 + -2.761904762 = 0.000000000 0.000000000 + x = 1.954122336 + -2.761904762 x = 1.954122336 + -2.761904762 Combine like terms: 1.954122336 + -2.761904762 = -0.807782426 x = -0.807782426 Simplifying x = -0.807782426Subproblem 2
x + 2.761904762 = -1.954122336 Simplifying x + 2.761904762 = -1.954122336 Reorder the terms: 2.761904762 + x = -1.954122336 Solving 2.761904762 + x = -1.954122336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.761904762' to each side of the equation. 2.761904762 + -2.761904762 + x = -1.954122336 + -2.761904762 Combine like terms: 2.761904762 + -2.761904762 = 0.000000000 0.000000000 + x = -1.954122336 + -2.761904762 x = -1.954122336 + -2.761904762 Combine like terms: -1.954122336 + -2.761904762 = -4.716027098 x = -4.716027098 Simplifying x = -4.716027098Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.807782426, -4.716027098}
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