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Simplifying (7x + -4)(3x + -4) = 2 Reorder the terms: (-4 + 7x)(3x + -4) = 2 Reorder the terms: (-4 + 7x)(-4 + 3x) = 2 Multiply (-4 + 7x) * (-4 + 3x) (-4(-4 + 3x) + 7x * (-4 + 3x)) = 2 ((-4 * -4 + 3x * -4) + 7x * (-4 + 3x)) = 2 ((16 + -12x) + 7x * (-4 + 3x)) = 2 (16 + -12x + (-4 * 7x + 3x * 7x)) = 2 (16 + -12x + (-28x + 21x2)) = 2 Combine like terms: -12x + -28x = -40x (16 + -40x + 21x2) = 2 Solving 16 + -40x + 21x2 = 2 Solving for variable 'x'. Reorder the terms: 16 + -2 + -40x + 21x2 = 2 + -2 Combine like terms: 16 + -2 = 14 14 + -40x + 21x2 = 2 + -2 Combine like terms: 2 + -2 = 0 14 + -40x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.6666666667 + -1.904761905x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -1.904761905x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -1.904761905x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -1.904761905x + x2 = 0 + -0.6666666667 -1.904761905x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -1.904761905x + x2 = -0.6666666667 The x term is -1.904761905x. Take half its coefficient (-0.9523809525). Square it (0.9070294787) and add it to both sides. Add '0.9070294787' to each side of the equation. -1.904761905x + 0.9070294787 + x2 = -0.6666666667 + 0.9070294787 Reorder the terms: 0.9070294787 + -1.904761905x + x2 = -0.6666666667 + 0.9070294787 Combine like terms: -0.6666666667 + 0.9070294787 = 0.240362812 0.9070294787 + -1.904761905x + x2 = 0.240362812 Factor a perfect square on the left side: (x + -0.9523809525)(x + -0.9523809525) = 0.240362812 Calculate the square root of the right side: 0.490268102 Break this problem into two subproblems by setting (x + -0.9523809525) equal to 0.490268102 and -0.490268102.Subproblem 1
x + -0.9523809525 = 0.490268102 Simplifying x + -0.9523809525 = 0.490268102 Reorder the terms: -0.9523809525 + x = 0.490268102 Solving -0.9523809525 + x = 0.490268102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9523809525' to each side of the equation. -0.9523809525 + 0.9523809525 + x = 0.490268102 + 0.9523809525 Combine like terms: -0.9523809525 + 0.9523809525 = 0.0000000000 0.0000000000 + x = 0.490268102 + 0.9523809525 x = 0.490268102 + 0.9523809525 Combine like terms: 0.490268102 + 0.9523809525 = 1.4426490545 x = 1.4426490545 Simplifying x = 1.4426490545Subproblem 2
x + -0.9523809525 = -0.490268102 Simplifying x + -0.9523809525 = -0.490268102 Reorder the terms: -0.9523809525 + x = -0.490268102 Solving -0.9523809525 + x = -0.490268102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9523809525' to each side of the equation. -0.9523809525 + 0.9523809525 + x = -0.490268102 + 0.9523809525 Combine like terms: -0.9523809525 + 0.9523809525 = 0.0000000000 0.0000000000 + x = -0.490268102 + 0.9523809525 x = -0.490268102 + 0.9523809525 Combine like terms: -0.490268102 + 0.9523809525 = 0.4621128505 x = 0.4621128505 Simplifying x = 0.4621128505Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4426490545, 0.4621128505}
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