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Simplifying (3x + -9)(x + 5) = x Reorder the terms: (-9 + 3x)(x + 5) = x Reorder the terms: (-9 + 3x)(5 + x) = x Multiply (-9 + 3x) * (5 + x) (-9(5 + x) + 3x * (5 + x)) = x ((5 * -9 + x * -9) + 3x * (5 + x)) = x ((-45 + -9x) + 3x * (5 + x)) = x (-45 + -9x + (5 * 3x + x * 3x)) = x (-45 + -9x + (15x + 3x2)) = x Combine like terms: -9x + 15x = 6x (-45 + 6x + 3x2) = x Solving -45 + 6x + 3x2 = x Solving for variable 'x'. Reorder the terms: -45 + 6x + -1x + 3x2 = x + -1x Combine like terms: 6x + -1x = 5x -45 + 5x + 3x2 = x + -1x Combine like terms: x + -1x = 0 -45 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -15 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 1.666666667x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 1.666666667x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 1.666666667x + x2 = 0 + 15 1.666666667x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 1.666666667x + x2 = 15 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 15 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 15 + 0.6944444447 Combine like terms: 15 + 0.6944444447 = 15.6944444447 0.6944444447 + 1.666666667x + x2 = 15.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 15.6944444447 Calculate the square root of the right side: 3.961621441 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 3.961621441 and -3.961621441.Subproblem 1
x + 0.8333333335 = 3.961621441 Simplifying x + 0.8333333335 = 3.961621441 Reorder the terms: 0.8333333335 + x = 3.961621441 Solving 0.8333333335 + x = 3.961621441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 3.961621441 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 3.961621441 + -0.8333333335 x = 3.961621441 + -0.8333333335 Combine like terms: 3.961621441 + -0.8333333335 = 3.1282881075 x = 3.1282881075 Simplifying x = 3.1282881075Subproblem 2
x + 0.8333333335 = -3.961621441 Simplifying x + 0.8333333335 = -3.961621441 Reorder the terms: 0.8333333335 + x = -3.961621441 Solving 0.8333333335 + x = -3.961621441 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -3.961621441 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -3.961621441 + -0.8333333335 x = -3.961621441 + -0.8333333335 Combine like terms: -3.961621441 + -0.8333333335 = -4.7949547745 x = -4.7949547745 Simplifying x = -4.7949547745Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1282881075, -4.7949547745}
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