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Simplifying 0 = 9x2 + -39x + 16 Reorder the terms: 0 = 16 + -39x + 9x2 Solving 0 = 16 + -39x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -16 = -16 -16 + 39x + -9x2 = 16 + -39x + 9x2 + -16 + 39x + -9x2 Reorder the terms: -16 + 39x + -9x2 = 16 + -16 + -39x + 39x + 9x2 + -9x2 Combine like terms: 16 + -16 = 0 -16 + 39x + -9x2 = 0 + -39x + 39x + 9x2 + -9x2 -16 + 39x + -9x2 = -39x + 39x + 9x2 + -9x2 Combine like terms: -39x + 39x = 0 -16 + 39x + -9x2 = 0 + 9x2 + -9x2 -16 + 39x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -16 + 39x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 1.777777778 + -4.333333333x + x2 = 0 Move the constant term to the right: Add '-1.777777778' to each side of the equation. 1.777777778 + -4.333333333x + -1.777777778 + x2 = 0 + -1.777777778 Reorder the terms: 1.777777778 + -1.777777778 + -4.333333333x + x2 = 0 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + -4.333333333x + x2 = 0 + -1.777777778 -4.333333333x + x2 = 0 + -1.777777778 Combine like terms: 0 + -1.777777778 = -1.777777778 -4.333333333x + x2 = -1.777777778 The x term is -4.333333333x. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333x + 4.694444446 + x2 = -1.777777778 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333x + x2 = -1.777777778 + 4.694444446 Combine like terms: -1.777777778 + 4.694444446 = 2.916666668 4.694444446 + -4.333333333x + x2 = 2.916666668 Factor a perfect square on the left side: (x + -2.166666667)(x + -2.166666667) = 2.916666668 Calculate the square root of the right side: 1.707825128 Break this problem into two subproblems by setting (x + -2.166666667) equal to 1.707825128 and -1.707825128.Subproblem 1
x + -2.166666667 = 1.707825128 Simplifying x + -2.166666667 = 1.707825128 Reorder the terms: -2.166666667 + x = 1.707825128 Solving -2.166666667 + x = 1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = 1.707825128 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 1.707825128 + 2.166666667 x = 1.707825128 + 2.166666667 Combine like terms: 1.707825128 + 2.166666667 = 3.874491795 x = 3.874491795 Simplifying x = 3.874491795Subproblem 2
x + -2.166666667 = -1.707825128 Simplifying x + -2.166666667 = -1.707825128 Reorder the terms: -2.166666667 + x = -1.707825128 Solving -2.166666667 + x = -1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = -1.707825128 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -1.707825128 + 2.166666667 x = -1.707825128 + 2.166666667 Combine like terms: -1.707825128 + 2.166666667 = 0.458841539 x = 0.458841539 Simplifying x = 0.458841539Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.874491795, 0.458841539}
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