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Simplifying 9x2 + 30x = 16 Reorder the terms: 30x + 9x2 = 16 Solving 30x + 9x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 30x + 9x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + 3.333333333x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + 3.333333333x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + 3.333333333x + x2 = 0 + 1.777777778 3.333333333x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 3.333333333x + x2 = 1.777777778 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 1.777777778 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 1.777777778 + 2.777777779 Combine like terms: 1.777777778 + 2.777777779 = 4.555555557 2.777777779 + 3.333333333x + x2 = 4.555555557 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 4.555555557 Calculate the square root of the right side: 2.134374746 Break this problem into two subproblems by setting (x + 1.666666667) equal to 2.134374746 and -2.134374746.Subproblem 1
x + 1.666666667 = 2.134374746 Simplifying x + 1.666666667 = 2.134374746 Reorder the terms: 1.666666667 + x = 2.134374746 Solving 1.666666667 + x = 2.134374746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 2.134374746 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 2.134374746 + -1.666666667 x = 2.134374746 + -1.666666667 Combine like terms: 2.134374746 + -1.666666667 = 0.467708079 x = 0.467708079 Simplifying x = 0.467708079Subproblem 2
x + 1.666666667 = -2.134374746 Simplifying x + 1.666666667 = -2.134374746 Reorder the terms: 1.666666667 + x = -2.134374746 Solving 1.666666667 + x = -2.134374746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -2.134374746 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -2.134374746 + -1.666666667 x = -2.134374746 + -1.666666667 Combine like terms: -2.134374746 + -1.666666667 = -3.801041413 x = -3.801041413 Simplifying x = -3.801041413Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.467708079, -3.801041413}
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