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Simplifying 4(x + 3)(2x + -3) = 9 Reorder the terms: 4(3 + x)(2x + -3) = 9 Reorder the terms: 4(3 + x)(-3 + 2x) = 9 Multiply (3 + x) * (-3 + 2x) 4(3(-3 + 2x) + x(-3 + 2x)) = 9 4((-3 * 3 + 2x * 3) + x(-3 + 2x)) = 9 4((-9 + 6x) + x(-3 + 2x)) = 9 4(-9 + 6x + (-3 * x + 2x * x)) = 9 4(-9 + 6x + (-3x + 2x2)) = 9 Combine like terms: 6x + -3x = 3x 4(-9 + 3x + 2x2) = 9 (-9 * 4 + 3x * 4 + 2x2 * 4) = 9 (-36 + 12x + 8x2) = 9 Solving -36 + 12x + 8x2 = 9 Solving for variable 'x'. Reorder the terms: -36 + -9 + 12x + 8x2 = 9 + -9 Combine like terms: -36 + -9 = -45 -45 + 12x + 8x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -45 + 12x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.625 + 1.5x + x2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + 1.5x + 5.625 + x2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + 1.5x + x2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + 1.5x + x2 = 0 + 5.625 1.5x + x2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 1.5x + x2 = 5.625 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 5.625 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 5.625 + 0.5625 Combine like terms: 5.625 + 0.5625 = 6.1875 0.5625 + 1.5x + x2 = 6.1875 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 6.1875 Calculate the square root of the right side: 2.487468593 Break this problem into two subproblems by setting (x + 0.75) equal to 2.487468593 and -2.487468593.Subproblem 1
x + 0.75 = 2.487468593 Simplifying x + 0.75 = 2.487468593 Reorder the terms: 0.75 + x = 2.487468593 Solving 0.75 + x = 2.487468593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.487468593 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.487468593 + -0.75 x = 2.487468593 + -0.75 Combine like terms: 2.487468593 + -0.75 = 1.737468593 x = 1.737468593 Simplifying x = 1.737468593Subproblem 2
x + 0.75 = -2.487468593 Simplifying x + 0.75 = -2.487468593 Reorder the terms: 0.75 + x = -2.487468593 Solving 0.75 + x = -2.487468593 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.487468593 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.487468593 + -0.75 x = -2.487468593 + -0.75 Combine like terms: -2.487468593 + -0.75 = -3.237468593 x = -3.237468593 Simplifying x = -3.237468593Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.737468593, -3.237468593}
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