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Simplifying (5x + 4)(x + -6) = 9 Reorder the terms: (4 + 5x)(x + -6) = 9 Reorder the terms: (4 + 5x)(-6 + x) = 9 Multiply (4 + 5x) * (-6 + x) (4(-6 + x) + 5x * (-6 + x)) = 9 ((-6 * 4 + x * 4) + 5x * (-6 + x)) = 9 ((-24 + 4x) + 5x * (-6 + x)) = 9 (-24 + 4x + (-6 * 5x + x * 5x)) = 9 (-24 + 4x + (-30x + 5x2)) = 9 Combine like terms: 4x + -30x = -26x (-24 + -26x + 5x2) = 9 Solving -24 + -26x + 5x2 = 9 Solving for variable 'x'. Reorder the terms: -24 + -9 + -26x + 5x2 = 9 + -9 Combine like terms: -24 + -9 = -33 -33 + -26x + 5x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -33 + -26x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.6 + -5.2x + x2 = 0 Move the constant term to the right: Add '6.6' to each side of the equation. -6.6 + -5.2x + 6.6 + x2 = 0 + 6.6 Reorder the terms: -6.6 + 6.6 + -5.2x + x2 = 0 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + -5.2x + x2 = 0 + 6.6 -5.2x + x2 = 0 + 6.6 Combine like terms: 0 + 6.6 = 6.6 -5.2x + x2 = 6.6 The x term is -5.2x. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2x + 6.76 + x2 = 6.6 + 6.76 Reorder the terms: 6.76 + -5.2x + x2 = 6.6 + 6.76 Combine like terms: 6.6 + 6.76 = 13.36 6.76 + -5.2x + x2 = 13.36 Factor a perfect square on the left side: (x + -2.6)(x + -2.6) = 13.36 Calculate the square root of the right side: 3.655133377 Break this problem into two subproblems by setting (x + -2.6) equal to 3.655133377 and -3.655133377.Subproblem 1
x + -2.6 = 3.655133377 Simplifying x + -2.6 = 3.655133377 Reorder the terms: -2.6 + x = 3.655133377 Solving -2.6 + x = 3.655133377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = 3.655133377 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = 3.655133377 + 2.6 x = 3.655133377 + 2.6 Combine like terms: 3.655133377 + 2.6 = 6.255133377 x = 6.255133377 Simplifying x = 6.255133377Subproblem 2
x + -2.6 = -3.655133377 Simplifying x + -2.6 = -3.655133377 Reorder the terms: -2.6 + x = -3.655133377 Solving -2.6 + x = -3.655133377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + x = -3.655133377 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + x = -3.655133377 + 2.6 x = -3.655133377 + 2.6 Combine like terms: -3.655133377 + 2.6 = -1.055133377 x = -1.055133377 Simplifying x = -1.055133377Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.255133377, -1.055133377}
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