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Simplifying (3x + -3)(7x + -4) = x Reorder the terms: (-3 + 3x)(7x + -4) = x Reorder the terms: (-3 + 3x)(-4 + 7x) = x Multiply (-3 + 3x) * (-4 + 7x) (-3(-4 + 7x) + 3x * (-4 + 7x)) = x ((-4 * -3 + 7x * -3) + 3x * (-4 + 7x)) = x ((12 + -21x) + 3x * (-4 + 7x)) = x (12 + -21x + (-4 * 3x + 7x * 3x)) = x (12 + -21x + (-12x + 21x2)) = x Combine like terms: -21x + -12x = -33x (12 + -33x + 21x2) = x Solving 12 + -33x + 21x2 = x Solving for variable 'x'. Reorder the terms: 12 + -33x + -1x + 21x2 = x + -1x Combine like terms: -33x + -1x = -34x 12 + -34x + 21x2 = x + -1x Combine like terms: x + -1x = 0 12 + -34x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.5714285714 + -1.619047619x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + -1.619047619x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + -1.619047619x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + -1.619047619x + x2 = 0 + -0.5714285714 -1.619047619x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 -1.619047619x + x2 = -0.5714285714 The x term is -1.619047619x. Take half its coefficient (-0.8095238095). Square it (0.6553287981) and add it to both sides. Add '0.6553287981' to each side of the equation. -1.619047619x + 0.6553287981 + x2 = -0.5714285714 + 0.6553287981 Reorder the terms: 0.6553287981 + -1.619047619x + x2 = -0.5714285714 + 0.6553287981 Combine like terms: -0.5714285714 + 0.6553287981 = 0.0839002267 0.6553287981 + -1.619047619x + x2 = 0.0839002267 Factor a perfect square on the left side: (x + -0.8095238095)(x + -0.8095238095) = 0.0839002267 Calculate the square root of the right side: 0.289655358 Break this problem into two subproblems by setting (x + -0.8095238095) equal to 0.289655358 and -0.289655358.Subproblem 1
x + -0.8095238095 = 0.289655358 Simplifying x + -0.8095238095 = 0.289655358 Reorder the terms: -0.8095238095 + x = 0.289655358 Solving -0.8095238095 + x = 0.289655358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8095238095' to each side of the equation. -0.8095238095 + 0.8095238095 + x = 0.289655358 + 0.8095238095 Combine like terms: -0.8095238095 + 0.8095238095 = 0.0000000000 0.0000000000 + x = 0.289655358 + 0.8095238095 x = 0.289655358 + 0.8095238095 Combine like terms: 0.289655358 + 0.8095238095 = 1.0991791675 x = 1.0991791675 Simplifying x = 1.0991791675Subproblem 2
x + -0.8095238095 = -0.289655358 Simplifying x + -0.8095238095 = -0.289655358 Reorder the terms: -0.8095238095 + x = -0.289655358 Solving -0.8095238095 + x = -0.289655358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8095238095' to each side of the equation. -0.8095238095 + 0.8095238095 + x = -0.289655358 + 0.8095238095 Combine like terms: -0.8095238095 + 0.8095238095 = 0.0000000000 0.0000000000 + x = -0.289655358 + 0.8095238095 x = -0.289655358 + 0.8095238095 Combine like terms: -0.289655358 + 0.8095238095 = 0.5198684515 x = 0.5198684515 Simplifying x = 0.5198684515Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0991791675, 0.5198684515}
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