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Simplifying (6x)(4 + -1x) = 20 Remove parenthesis around (6x) 6x(4 + -1x) = 20 (4 * 6x + -1x * 6x) = 20 (24x + -6x2) = 20 Solving 24x + -6x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 24x + -6x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 24x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 12x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 12x + -3x2)' equal to zero and attempt to solve: Simplifying -10 + 12x + -3x2 = 0 Solving -10 + 12x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 3.333333333 + -4x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -4x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -4x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -4x + x2 = 0 + -3.333333333 -4x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -4x + x2 = -3.333333333 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -3.333333333 + 4 Reorder the terms: 4 + -4x + x2 = -3.333333333 + 4 Combine like terms: -3.333333333 + 4 = 0.666666667 4 + -4x + x2 = 0.666666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.666666667 Calculate the square root of the right side: 0.816496581 Break this problem into two subproblems by setting (x + -2) equal to 0.816496581 and -0.816496581.Subproblem 1
x + -2 = 0.816496581 Simplifying x + -2 = 0.816496581 Reorder the terms: -2 + x = 0.816496581 Solving -2 + x = 0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.816496581 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.816496581 + 2 x = 0.816496581 + 2 Combine like terms: 0.816496581 + 2 = 2.816496581 x = 2.816496581 Simplifying x = 2.816496581Subproblem 2
x + -2 = -0.816496581 Simplifying x + -2 = -0.816496581 Reorder the terms: -2 + x = -0.816496581 Solving -2 + x = -0.816496581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.816496581 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.816496581 + 2 x = -0.816496581 + 2 Combine like terms: -0.816496581 + 2 = 1.183503419 x = 1.183503419 Simplifying x = 1.183503419Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.816496581, 1.183503419}Solution
x = {2.816496581, 1.183503419}
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