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Simplifying (2x + 3)(2x + -5) + -3(x + 5)(3x + -5) = 22x + 10 Reorder the terms: (3 + 2x)(2x + -5) + -3(x + 5)(3x + -5) = 22x + 10 Reorder the terms: (3 + 2x)(-5 + 2x) + -3(x + 5)(3x + -5) = 22x + 10 Multiply (3 + 2x) * (-5 + 2x) (3(-5 + 2x) + 2x * (-5 + 2x)) + -3(x + 5)(3x + -5) = 22x + 10 ((-5 * 3 + 2x * 3) + 2x * (-5 + 2x)) + -3(x + 5)(3x + -5) = 22x + 10 ((-15 + 6x) + 2x * (-5 + 2x)) + -3(x + 5)(3x + -5) = 22x + 10 (-15 + 6x + (-5 * 2x + 2x * 2x)) + -3(x + 5)(3x + -5) = 22x + 10 (-15 + 6x + (-10x + 4x2)) + -3(x + 5)(3x + -5) = 22x + 10 Combine like terms: 6x + -10x = -4x (-15 + -4x + 4x2) + -3(x + 5)(3x + -5) = 22x + 10 Reorder the terms: -15 + -4x + 4x2 + -3(5 + x)(3x + -5) = 22x + 10 Reorder the terms: -15 + -4x + 4x2 + -3(5 + x)(-5 + 3x) = 22x + 10 Multiply (5 + x) * (-5 + 3x) -15 + -4x + 4x2 + -3(5(-5 + 3x) + x(-5 + 3x)) = 22x + 10 -15 + -4x + 4x2 + -3((-5 * 5 + 3x * 5) + x(-5 + 3x)) = 22x + 10 -15 + -4x + 4x2 + -3((-25 + 15x) + x(-5 + 3x)) = 22x + 10 -15 + -4x + 4x2 + -3(-25 + 15x + (-5 * x + 3x * x)) = 22x + 10 -15 + -4x + 4x2 + -3(-25 + 15x + (-5x + 3x2)) = 22x + 10 Combine like terms: 15x + -5x = 10x -15 + -4x + 4x2 + -3(-25 + 10x + 3x2) = 22x + 10 -15 + -4x + 4x2 + (-25 * -3 + 10x * -3 + 3x2 * -3) = 22x + 10 -15 + -4x + 4x2 + (75 + -30x + -9x2) = 22x + 10 Reorder the terms: -15 + 75 + -4x + -30x + 4x2 + -9x2 = 22x + 10 Combine like terms: -15 + 75 = 60 60 + -4x + -30x + 4x2 + -9x2 = 22x + 10 Combine like terms: -4x + -30x = -34x 60 + -34x + 4x2 + -9x2 = 22x + 10 Combine like terms: 4x2 + -9x2 = -5x2 60 + -34x + -5x2 = 22x + 10 Reorder the terms: 60 + -34x + -5x2 = 10 + 22x Solving 60 + -34x + -5x2 = 10 + 22x Solving for variable 'x'. Reorder the terms: 60 + -10 + -34x + -22x + -5x2 = 10 + 22x + -10 + -22x Combine like terms: 60 + -10 = 50 50 + -34x + -22x + -5x2 = 10 + 22x + -10 + -22x Combine like terms: -34x + -22x = -56x 50 + -56x + -5x2 = 10 + 22x + -10 + -22x Reorder the terms: 50 + -56x + -5x2 = 10 + -10 + 22x + -22x Combine like terms: 10 + -10 = 0 50 + -56x + -5x2 = 0 + 22x + -22x 50 + -56x + -5x2 = 22x + -22x Combine like terms: 22x + -22x = 0 50 + -56x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -10 + 11.2x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 11.2x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 11.2x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 11.2x + x2 = 0 + 10 11.2x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 11.2x + x2 = 10 The x term is 11.2x. Take half its coefficient (5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. 11.2x + 31.36 + x2 = 10 + 31.36 Reorder the terms: 31.36 + 11.2x + x2 = 10 + 31.36 Combine like terms: 10 + 31.36 = 41.36 31.36 + 11.2x + x2 = 41.36 Factor a perfect square on the left side: (x + 5.6)(x + 5.6) = 41.36 Calculate the square root of the right side: 6.431174076 Break this problem into two subproblems by setting (x + 5.6) equal to 6.431174076 and -6.431174076.Subproblem 1
x + 5.6 = 6.431174076 Simplifying x + 5.6 = 6.431174076 Reorder the terms: 5.6 + x = 6.431174076 Solving 5.6 + x = 6.431174076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = 6.431174076 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = 6.431174076 + -5.6 x = 6.431174076 + -5.6 Combine like terms: 6.431174076 + -5.6 = 0.831174076 x = 0.831174076 Simplifying x = 0.831174076Subproblem 2
x + 5.6 = -6.431174076 Simplifying x + 5.6 = -6.431174076 Reorder the terms: 5.6 + x = -6.431174076 Solving 5.6 + x = -6.431174076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = -6.431174076 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = -6.431174076 + -5.6 x = -6.431174076 + -5.6 Combine like terms: -6.431174076 + -5.6 = -12.031174076 x = -12.031174076 Simplifying x = -12.031174076Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.831174076, -12.031174076}
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