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Simplifying (6x + -2) * 7x = 180 Reorder the terms: (-2 + 6x) * 7x = 180 Reorder the terms for easier multiplication: 7x(-2 + 6x) = 180 (-2 * 7x + 6x * 7x) = 180 (-14x + 42x2) = 180 Solving -14x + 42x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -14x + 42x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -14x + 42x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + -7x + 21x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + -7x + 21x2)' equal to zero and attempt to solve: Simplifying -90 + -7x + 21x2 = 0 Solving -90 + -7x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -4.285714286 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + -0.3333333333x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + -0.3333333333x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + -0.3333333333x + x2 = 0 + 4.285714286 -0.3333333333x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 -0.3333333333x + x2 = 4.285714286 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 4.285714286 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 4.285714286 + 0.02777777779 Combine like terms: 4.285714286 + 0.02777777779 = 4.31349206379 0.02777777779 + -0.3333333333x + x2 = 4.31349206379 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 4.31349206379 Calculate the square root of the right side: 2.076894813 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 2.076894813 and -2.076894813.Subproblem 1
x + -0.1666666667 = 2.076894813 Simplifying x + -0.1666666667 = 2.076894813 Reorder the terms: -0.1666666667 + x = 2.076894813 Solving -0.1666666667 + x = 2.076894813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 2.076894813 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 2.076894813 + 0.1666666667 x = 2.076894813 + 0.1666666667 Combine like terms: 2.076894813 + 0.1666666667 = 2.2435614797 x = 2.2435614797 Simplifying x = 2.2435614797Subproblem 2
x + -0.1666666667 = -2.076894813 Simplifying x + -0.1666666667 = -2.076894813 Reorder the terms: -0.1666666667 + x = -2.076894813 Solving -0.1666666667 + x = -2.076894813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -2.076894813 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -2.076894813 + 0.1666666667 x = -2.076894813 + 0.1666666667 Combine like terms: -2.076894813 + 0.1666666667 = -1.9102281463 x = -1.9102281463 Simplifying x = -1.9102281463Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2435614797, -1.9102281463}Solution
x = {2.2435614797, -1.9102281463}
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