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Simplifying 12 = 2x(x + -7) Reorder the terms: 12 = 2x(-7 + x) 12 = (-7 * 2x + x * 2x) 12 = (-14x + 2x2) Solving 12 = -14x + 2x2 Solving for variable 'x'. Reorder the terms: 12 + 14x + -2x2 = -14x + 14x + 2x2 + -2x2 Combine like terms: -14x + 14x = 0 12 + 14x + -2x2 = 0 + 2x2 + -2x2 12 + 14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 12 + 14x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 7x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying 6 + 7x + -1x2 = 0 Solving 6 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + -7x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -7x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -7x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7x + x2 = 0 + 6 -7x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -7x + x2 = 6 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 6 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 6 + 12.25 Combine like terms: 6 + 12.25 = 18.25 12.25 + -7x + x2 = 18.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + -3.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + -3.5 = 4.272001873 Simplifying x + -3.5 = 4.272001873 Reorder the terms: -3.5 + x = 4.272001873 Solving -3.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.272001873 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.272001873 + 3.5 x = 4.272001873 + 3.5 Combine like terms: 4.272001873 + 3.5 = 7.772001873 x = 7.772001873 Simplifying x = 7.772001873Subproblem 2
x + -3.5 = -4.272001873 Simplifying x + -3.5 = -4.272001873 Reorder the terms: -3.5 + x = -4.272001873 Solving -3.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.272001873 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.272001873 + 3.5 x = -4.272001873 + 3.5 Combine like terms: -4.272001873 + 3.5 = -0.772001873 x = -0.772001873 Simplifying x = -0.772001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.772001873, -0.772001873}Solution
x = {7.772001873, -0.772001873}
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