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Simplifying 9x(2x + -3) = 3(x + 1) + 4x Reorder the terms: 9x(-3 + 2x) = 3(x + 1) + 4x (-3 * 9x + 2x * 9x) = 3(x + 1) + 4x (-27x + 18x2) = 3(x + 1) + 4x Reorder the terms: -27x + 18x2 = 3(1 + x) + 4x -27x + 18x2 = (1 * 3 + x * 3) + 4x -27x + 18x2 = (3 + 3x) + 4x Combine like terms: 3x + 4x = 7x -27x + 18x2 = 3 + 7x Solving -27x + 18x2 = 3 + 7x Solving for variable 'x'. Reorder the terms: -3 + -27x + -7x + 18x2 = 3 + 7x + -3 + -7x Combine like terms: -27x + -7x = -34x -3 + -34x + 18x2 = 3 + 7x + -3 + -7x Reorder the terms: -3 + -34x + 18x2 = 3 + -3 + 7x + -7x Combine like terms: 3 + -3 = 0 -3 + -34x + 18x2 = 0 + 7x + -7x -3 + -34x + 18x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -3 + -34x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.1666666667 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -1.888888889x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -1.888888889x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -1.888888889x + x2 = 0 + 0.1666666667 -1.888888889x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -1.888888889x + x2 = 0.1666666667 The x term is -1.888888889x. Take half its coefficient (-0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. -1.888888889x + 0.8919753087 + x2 = 0.1666666667 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = 0.1666666667 + 0.8919753087 Combine like terms: 0.1666666667 + 0.8919753087 = 1.0586419754 0.8919753087 + -1.888888889x + x2 = 1.0586419754 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 1.0586419754 Calculate the square root of the right side: 1.028903288 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 1.028903288 and -1.028903288.Subproblem 1
x + -0.9444444445 = 1.028903288 Simplifying x + -0.9444444445 = 1.028903288 Reorder the terms: -0.9444444445 + x = 1.028903288 Solving -0.9444444445 + x = 1.028903288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = 1.028903288 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 1.028903288 + 0.9444444445 x = 1.028903288 + 0.9444444445 Combine like terms: 1.028903288 + 0.9444444445 = 1.9733477325 x = 1.9733477325 Simplifying x = 1.9733477325Subproblem 2
x + -0.9444444445 = -1.028903288 Simplifying x + -0.9444444445 = -1.028903288 Reorder the terms: -0.9444444445 + x = -1.028903288 Solving -0.9444444445 + x = -1.028903288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = -1.028903288 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -1.028903288 + 0.9444444445 x = -1.028903288 + 0.9444444445 Combine like terms: -1.028903288 + 0.9444444445 = -0.0844588435 x = -0.0844588435 Simplifying x = -0.0844588435Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9733477325, -0.0844588435}
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