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Simplifying 3x(7x + -5) + 5 = 15 + 16x Reorder the terms: 3x(-5 + 7x) + 5 = 15 + 16x (-5 * 3x + 7x * 3x) + 5 = 15 + 16x (-15x + 21x2) + 5 = 15 + 16x Reorder the terms: 5 + -15x + 21x2 = 15 + 16x Solving 5 + -15x + 21x2 = 15 + 16x Solving for variable 'x'. Reorder the terms: 5 + -15 + -15x + -16x + 21x2 = 15 + 16x + -15 + -16x Combine like terms: 5 + -15 = -10 -10 + -15x + -16x + 21x2 = 15 + 16x + -15 + -16x Combine like terms: -15x + -16x = -31x -10 + -31x + 21x2 = 15 + 16x + -15 + -16x Reorder the terms: -10 + -31x + 21x2 = 15 + -15 + 16x + -16x Combine like terms: 15 + -15 = 0 -10 + -31x + 21x2 = 0 + 16x + -16x -10 + -31x + 21x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -10 + -31x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.4761904762 + -1.476190476x + x2 = 0 Move the constant term to the right: Add '0.4761904762' to each side of the equation. -0.4761904762 + -1.476190476x + 0.4761904762 + x2 = 0 + 0.4761904762 Reorder the terms: -0.4761904762 + 0.4761904762 + -1.476190476x + x2 = 0 + 0.4761904762 Combine like terms: -0.4761904762 + 0.4761904762 = 0.0000000000 0.0000000000 + -1.476190476x + x2 = 0 + 0.4761904762 -1.476190476x + x2 = 0 + 0.4761904762 Combine like terms: 0 + 0.4761904762 = 0.4761904762 -1.476190476x + x2 = 0.4761904762 The x term is -1.476190476x. Take half its coefficient (-0.738095238). Square it (0.5447845804) and add it to both sides. Add '0.5447845804' to each side of the equation. -1.476190476x + 0.5447845804 + x2 = 0.4761904762 + 0.5447845804 Reorder the terms: 0.5447845804 + -1.476190476x + x2 = 0.4761904762 + 0.5447845804 Combine like terms: 0.4761904762 + 0.5447845804 = 1.0209750566 0.5447845804 + -1.476190476x + x2 = 1.0209750566 Factor a perfect square on the left side: (x + -0.738095238)(x + -0.738095238) = 1.0209750566 Calculate the square root of the right side: 1.010433103 Break this problem into two subproblems by setting (x + -0.738095238) equal to 1.010433103 and -1.010433103.Subproblem 1
x + -0.738095238 = 1.010433103 Simplifying x + -0.738095238 = 1.010433103 Reorder the terms: -0.738095238 + x = 1.010433103 Solving -0.738095238 + x = 1.010433103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.738095238' to each side of the equation. -0.738095238 + 0.738095238 + x = 1.010433103 + 0.738095238 Combine like terms: -0.738095238 + 0.738095238 = 0.000000000 0.000000000 + x = 1.010433103 + 0.738095238 x = 1.010433103 + 0.738095238 Combine like terms: 1.010433103 + 0.738095238 = 1.748528341 x = 1.748528341 Simplifying x = 1.748528341Subproblem 2
x + -0.738095238 = -1.010433103 Simplifying x + -0.738095238 = -1.010433103 Reorder the terms: -0.738095238 + x = -1.010433103 Solving -0.738095238 + x = -1.010433103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.738095238' to each side of the equation. -0.738095238 + 0.738095238 + x = -1.010433103 + 0.738095238 Combine like terms: -0.738095238 + 0.738095238 = 0.000000000 0.000000000 + x = -1.010433103 + 0.738095238 x = -1.010433103 + 0.738095238 Combine like terms: -1.010433103 + 0.738095238 = -0.272337865 x = -0.272337865 Simplifying x = -0.272337865Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.748528341, -0.272337865}
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