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Simplifying (5x + 1)(x + -9) = (9x + -80) Reorder the terms: (1 + 5x)(x + -9) = (9x + -80) Reorder the terms: (1 + 5x)(-9 + x) = (9x + -80) Multiply (1 + 5x) * (-9 + x) (1(-9 + x) + 5x * (-9 + x)) = (9x + -80) ((-9 * 1 + x * 1) + 5x * (-9 + x)) = (9x + -80) ((-9 + 1x) + 5x * (-9 + x)) = (9x + -80) (-9 + 1x + (-9 * 5x + x * 5x)) = (9x + -80) (-9 + 1x + (-45x + 5x2)) = (9x + -80) Combine like terms: 1x + -45x = -44x (-9 + -44x + 5x2) = (9x + -80) Reorder the terms: -9 + -44x + 5x2 = (-80 + 9x) Remove parenthesis around (-80 + 9x) -9 + -44x + 5x2 = -80 + 9x Solving -9 + -44x + 5x2 = -80 + 9x Solving for variable 'x'. Reorder the terms: -9 + 80 + -44x + -9x + 5x2 = -80 + 9x + 80 + -9x Combine like terms: -9 + 80 = 71 71 + -44x + -9x + 5x2 = -80 + 9x + 80 + -9x Combine like terms: -44x + -9x = -53x 71 + -53x + 5x2 = -80 + 9x + 80 + -9x Reorder the terms: 71 + -53x + 5x2 = -80 + 80 + 9x + -9x Combine like terms: -80 + 80 = 0 71 + -53x + 5x2 = 0 + 9x + -9x 71 + -53x + 5x2 = 9x + -9x Combine like terms: 9x + -9x = 0 71 + -53x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 14.2 + -10.6x + x2 = 0 Move the constant term to the right: Add '-14.2' to each side of the equation. 14.2 + -10.6x + -14.2 + x2 = 0 + -14.2 Reorder the terms: 14.2 + -14.2 + -10.6x + x2 = 0 + -14.2 Combine like terms: 14.2 + -14.2 = 0.0 0.0 + -10.6x + x2 = 0 + -14.2 -10.6x + x2 = 0 + -14.2 Combine like terms: 0 + -14.2 = -14.2 -10.6x + x2 = -14.2 The x term is -10.6x. Take half its coefficient (-5.3). Square it (28.09) and add it to both sides. Add '28.09' to each side of the equation. -10.6x + 28.09 + x2 = -14.2 + 28.09 Reorder the terms: 28.09 + -10.6x + x2 = -14.2 + 28.09 Combine like terms: -14.2 + 28.09 = 13.89 28.09 + -10.6x + x2 = 13.89 Factor a perfect square on the left side: (x + -5.3)(x + -5.3) = 13.89 Calculate the square root of the right side: 3.726929031 Break this problem into two subproblems by setting (x + -5.3) equal to 3.726929031 and -3.726929031.Subproblem 1
x + -5.3 = 3.726929031 Simplifying x + -5.3 = 3.726929031 Reorder the terms: -5.3 + x = 3.726929031 Solving -5.3 + x = 3.726929031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.3' to each side of the equation. -5.3 + 5.3 + x = 3.726929031 + 5.3 Combine like terms: -5.3 + 5.3 = 0.0 0.0 + x = 3.726929031 + 5.3 x = 3.726929031 + 5.3 Combine like terms: 3.726929031 + 5.3 = 9.026929031 x = 9.026929031 Simplifying x = 9.026929031Subproblem 2
x + -5.3 = -3.726929031 Simplifying x + -5.3 = -3.726929031 Reorder the terms: -5.3 + x = -3.726929031 Solving -5.3 + x = -3.726929031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.3' to each side of the equation. -5.3 + 5.3 + x = -3.726929031 + 5.3 Combine like terms: -5.3 + 5.3 = 0.0 0.0 + x = -3.726929031 + 5.3 x = -3.726929031 + 5.3 Combine like terms: -3.726929031 + 5.3 = 1.573070969 x = 1.573070969 Simplifying x = 1.573070969Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.026929031, 1.573070969}
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