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Simplifying 16x + -3x2 = 15 Solving 16x + -3x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 16x + -3x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 16x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 5 + -5.333333333x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -5.333333333x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -5.333333333x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5.333333333x + x2 = 0 + -5 -5.333333333x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5.333333333x + x2 = -5 The x term is -5.333333333x. Take half its coefficient (-2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. -5.333333333x + 7.111111113 + x2 = -5 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333x + x2 = -5 + 7.111111113 Combine like terms: -5 + 7.111111113 = 2.111111113 7.111111113 + -5.333333333x + x2 = 2.111111113 Factor a perfect square on the left side: (x + -2.666666667)(x + -2.666666667) = 2.111111113 Calculate the square root of the right side: 1.452966315 Break this problem into two subproblems by setting (x + -2.666666667) equal to 1.452966315 and -1.452966315.Subproblem 1
x + -2.666666667 = 1.452966315 Simplifying x + -2.666666667 = 1.452966315 Reorder the terms: -2.666666667 + x = 1.452966315 Solving -2.666666667 + x = 1.452966315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x = 1.452966315 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = 1.452966315 + 2.666666667 x = 1.452966315 + 2.666666667 Combine like terms: 1.452966315 + 2.666666667 = 4.119632982 x = 4.119632982 Simplifying x = 4.119632982Subproblem 2
x + -2.666666667 = -1.452966315 Simplifying x + -2.666666667 = -1.452966315 Reorder the terms: -2.666666667 + x = -1.452966315 Solving -2.666666667 + x = -1.452966315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x = -1.452966315 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = -1.452966315 + 2.666666667 x = -1.452966315 + 2.666666667 Combine like terms: -1.452966315 + 2.666666667 = 1.213700352 x = 1.213700352 Simplifying x = 1.213700352Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.119632982, 1.213700352}
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