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Simplifying (5x + 12)(7x + -4) = 50 Reorder the terms: (12 + 5x)(7x + -4) = 50 Reorder the terms: (12 + 5x)(-4 + 7x) = 50 Multiply (12 + 5x) * (-4 + 7x) (12(-4 + 7x) + 5x * (-4 + 7x)) = 50 ((-4 * 12 + 7x * 12) + 5x * (-4 + 7x)) = 50 ((-48 + 84x) + 5x * (-4 + 7x)) = 50 (-48 + 84x + (-4 * 5x + 7x * 5x)) = 50 (-48 + 84x + (-20x + 35x2)) = 50 Combine like terms: 84x + -20x = 64x (-48 + 64x + 35x2) = 50 Solving -48 + 64x + 35x2 = 50 Solving for variable 'x'. Reorder the terms: -48 + -50 + 64x + 35x2 = 50 + -50 Combine like terms: -48 + -50 = -98 -98 + 64x + 35x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -98 + 64x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -2.8 + 1.828571429x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + 1.828571429x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + 1.828571429x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + 1.828571429x + x2 = 0 + 2.8 1.828571429x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 1.828571429x + x2 = 2.8 The x term is 1.828571429x. Take half its coefficient (0.9142857145). Square it (0.8359183677) and add it to both sides. Add '0.8359183677' to each side of the equation. 1.828571429x + 0.8359183677 + x2 = 2.8 + 0.8359183677 Reorder the terms: 0.8359183677 + 1.828571429x + x2 = 2.8 + 0.8359183677 Combine like terms: 2.8 + 0.8359183677 = 3.6359183677 0.8359183677 + 1.828571429x + x2 = 3.6359183677 Factor a perfect square on the left side: (x + 0.9142857145)(x + 0.9142857145) = 3.6359183677 Calculate the square root of the right side: 1.906808424 Break this problem into two subproblems by setting (x + 0.9142857145) equal to 1.906808424 and -1.906808424.Subproblem 1
x + 0.9142857145 = 1.906808424 Simplifying x + 0.9142857145 = 1.906808424 Reorder the terms: 0.9142857145 + x = 1.906808424 Solving 0.9142857145 + x = 1.906808424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9142857145' to each side of the equation. 0.9142857145 + -0.9142857145 + x = 1.906808424 + -0.9142857145 Combine like terms: 0.9142857145 + -0.9142857145 = 0.0000000000 0.0000000000 + x = 1.906808424 + -0.9142857145 x = 1.906808424 + -0.9142857145 Combine like terms: 1.906808424 + -0.9142857145 = 0.9925227095 x = 0.9925227095 Simplifying x = 0.9925227095Subproblem 2
x + 0.9142857145 = -1.906808424 Simplifying x + 0.9142857145 = -1.906808424 Reorder the terms: 0.9142857145 + x = -1.906808424 Solving 0.9142857145 + x = -1.906808424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9142857145' to each side of the equation. 0.9142857145 + -0.9142857145 + x = -1.906808424 + -0.9142857145 Combine like terms: 0.9142857145 + -0.9142857145 = 0.0000000000 0.0000000000 + x = -1.906808424 + -0.9142857145 x = -1.906808424 + -0.9142857145 Combine like terms: -1.906808424 + -0.9142857145 = -2.8210941385 x = -2.8210941385 Simplifying x = -2.8210941385Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9925227095, -2.8210941385}
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