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Simplifying (5x + 7)(2x + -14) = 6 Reorder the terms: (7 + 5x)(2x + -14) = 6 Reorder the terms: (7 + 5x)(-14 + 2x) = 6 Multiply (7 + 5x) * (-14 + 2x) (7(-14 + 2x) + 5x * (-14 + 2x)) = 6 ((-14 * 7 + 2x * 7) + 5x * (-14 + 2x)) = 6 ((-98 + 14x) + 5x * (-14 + 2x)) = 6 (-98 + 14x + (-14 * 5x + 2x * 5x)) = 6 (-98 + 14x + (-70x + 10x2)) = 6 Combine like terms: 14x + -70x = -56x (-98 + -56x + 10x2) = 6 Solving -98 + -56x + 10x2 = 6 Solving for variable 'x'. Reorder the terms: -98 + -6 + -56x + 10x2 = 6 + -6 Combine like terms: -98 + -6 = -104 -104 + -56x + 10x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -104 + -56x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-52 + -28x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-52 + -28x + 5x2)' equal to zero and attempt to solve: Simplifying -52 + -28x + 5x2 = 0 Solving -52 + -28x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10.4 + -5.6x + x2 = 0 Move the constant term to the right: Add '10.4' to each side of the equation. -10.4 + -5.6x + 10.4 + x2 = 0 + 10.4 Reorder the terms: -10.4 + 10.4 + -5.6x + x2 = 0 + 10.4 Combine like terms: -10.4 + 10.4 = 0.0 0.0 + -5.6x + x2 = 0 + 10.4 -5.6x + x2 = 0 + 10.4 Combine like terms: 0 + 10.4 = 10.4 -5.6x + x2 = 10.4 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = 10.4 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = 10.4 + 7.84 Combine like terms: 10.4 + 7.84 = 18.24 7.84 + -5.6x + x2 = 18.24 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 18.24 Calculate the square root of the right side: 4.270831301 Break this problem into two subproblems by setting (x + -2.8) equal to 4.270831301 and -4.270831301.Subproblem 1
x + -2.8 = 4.270831301 Simplifying x + -2.8 = 4.270831301 Reorder the terms: -2.8 + x = 4.270831301 Solving -2.8 + x = 4.270831301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 4.270831301 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 4.270831301 + 2.8 x = 4.270831301 + 2.8 Combine like terms: 4.270831301 + 2.8 = 7.070831301 x = 7.070831301 Simplifying x = 7.070831301Subproblem 2
x + -2.8 = -4.270831301 Simplifying x + -2.8 = -4.270831301 Reorder the terms: -2.8 + x = -4.270831301 Solving -2.8 + x = -4.270831301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -4.270831301 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -4.270831301 + 2.8 x = -4.270831301 + 2.8 Combine like terms: -4.270831301 + 2.8 = -1.470831301 x = -1.470831301 Simplifying x = -1.470831301Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.070831301, -1.470831301}Solution
x = {7.070831301, -1.470831301}
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