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Simplifying -72 = 5x(-14x + 36) Reorder the terms: -72 = 5x(36 + -14x) -72 = (36 * 5x + -14x * 5x) -72 = (180x + -70x2) Solving -72 = 180x + -70x2 Solving for variable 'x'. Reorder the terms: -72 + -180x + 70x2 = 180x + -180x + -70x2 + 70x2 Combine like terms: 180x + -180x = 0 -72 + -180x + 70x2 = 0 + -70x2 + 70x2 -72 + -180x + 70x2 = -70x2 + 70x2 Combine like terms: -70x2 + 70x2 = 0 -72 + -180x + 70x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + -90x + 35x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + -90x + 35x2)' equal to zero and attempt to solve: Simplifying -36 + -90x + 35x2 = 0 Solving -36 + -90x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -1.028571429 + -2.571428571x + x2 = 0 Move the constant term to the right: Add '1.028571429' to each side of the equation. -1.028571429 + -2.571428571x + 1.028571429 + x2 = 0 + 1.028571429 Reorder the terms: -1.028571429 + 1.028571429 + -2.571428571x + x2 = 0 + 1.028571429 Combine like terms: -1.028571429 + 1.028571429 = 0.000000000 0.000000000 + -2.571428571x + x2 = 0 + 1.028571429 -2.571428571x + x2 = 0 + 1.028571429 Combine like terms: 0 + 1.028571429 = 1.028571429 -2.571428571x + x2 = 1.028571429 The x term is -2.571428571x. Take half its coefficient (-1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. -2.571428571x + 1.653061225 + x2 = 1.028571429 + 1.653061225 Reorder the terms: 1.653061225 + -2.571428571x + x2 = 1.028571429 + 1.653061225 Combine like terms: 1.028571429 + 1.653061225 = 2.681632654 1.653061225 + -2.571428571x + x2 = 2.681632654 Factor a perfect square on the left side: (x + -1.285714286)(x + -1.285714286) = 2.681632654 Calculate the square root of the right side: 1.63756913 Break this problem into two subproblems by setting (x + -1.285714286) equal to 1.63756913 and -1.63756913.Subproblem 1
x + -1.285714286 = 1.63756913 Simplifying x + -1.285714286 = 1.63756913 Reorder the terms: -1.285714286 + x = 1.63756913 Solving -1.285714286 + x = 1.63756913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.285714286' to each side of the equation. -1.285714286 + 1.285714286 + x = 1.63756913 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = 1.63756913 + 1.285714286 x = 1.63756913 + 1.285714286 Combine like terms: 1.63756913 + 1.285714286 = 2.923283416 x = 2.923283416 Simplifying x = 2.923283416Subproblem 2
x + -1.285714286 = -1.63756913 Simplifying x + -1.285714286 = -1.63756913 Reorder the terms: -1.285714286 + x = -1.63756913 Solving -1.285714286 + x = -1.63756913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.285714286' to each side of the equation. -1.285714286 + 1.285714286 + x = -1.63756913 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + x = -1.63756913 + 1.285714286 x = -1.63756913 + 1.285714286 Combine like terms: -1.63756913 + 1.285714286 = -0.351854844 x = -0.351854844 Simplifying x = -0.351854844Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.923283416, -0.351854844}Solution
x = {2.923283416, -0.351854844}
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