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Simplifying 6x2 + 10x + -16 = 3 Reorder the terms: -16 + 10x + 6x2 = 3 Solving -16 + 10x + 6x2 = 3 Solving for variable 'x'. Reorder the terms: -16 + -3 + 10x + 6x2 = 3 + -3 Combine like terms: -16 + -3 = -19 -19 + 10x + 6x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -19 + 10x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -3.166666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '3.166666667' to each side of the equation. -3.166666667 + 1.666666667x + 3.166666667 + x2 = 0 + 3.166666667 Reorder the terms: -3.166666667 + 3.166666667 + 1.666666667x + x2 = 0 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 3.166666667 1.666666667x + x2 = 0 + 3.166666667 Combine like terms: 0 + 3.166666667 = 3.166666667 1.666666667x + x2 = 3.166666667 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 = 3.166666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 3.166666667 + 0.6944444447 Combine like terms: 3.166666667 + 0.6944444447 = 3.8611111117 0.6944444447 + 1.666666667x + x2 = 3.8611111117 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 3.8611111117 Calculate the square root of the right side: 1.964971021 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.964971021 and -1.964971021.Subproblem 1
x + 0.8333333335 = 1.964971021 Simplifying x + 0.8333333335 = 1.964971021 Reorder the terms: 0.8333333335 + x = 1.964971021 Solving 0.8333333335 + x = 1.964971021 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 = 1.964971021 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.964971021 + -0.8333333335 x = 1.964971021 + -0.8333333335 Combine like terms: 1.964971021 + -0.8333333335 = 1.1316376875 x = 1.1316376875 Simplifying x = 1.1316376875Subproblem 2
x + 0.8333333335 = -1.964971021 Simplifying x + 0.8333333335 = -1.964971021 Reorder the terms: 0.8333333335 + x = -1.964971021 Solving 0.8333333335 + x = -1.964971021 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 = -1.964971021 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.964971021 + -0.8333333335 x = -1.964971021 + -0.8333333335 Combine like terms: -1.964971021 + -0.8333333335 = -2.7983043545 x = -2.7983043545 Simplifying x = -2.7983043545Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1316376875, -2.7983043545}
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