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Simplifying 14x4 + 118x3 + 72x2 = 0 Reorder the terms: 72x2 + 118x3 + 14x4 = 0 Solving 72x2 + 118x3 + 14x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(36 + 59x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(36 + 59x + 7x2)' equal to zero and attempt to solve: Simplifying 36 + 59x + 7x2 = 0 Solving 36 + 59x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 5.142857143 + 8.428571429x + x2 = 0 Move the constant term to the right: Add '-5.142857143' to each side of the equation. 5.142857143 + 8.428571429x + -5.142857143 + x2 = 0 + -5.142857143 Reorder the terms: 5.142857143 + -5.142857143 + 8.428571429x + x2 = 0 + -5.142857143 Combine like terms: 5.142857143 + -5.142857143 = 0.000000000 0.000000000 + 8.428571429x + x2 = 0 + -5.142857143 8.428571429x + x2 = 0 + -5.142857143 Combine like terms: 0 + -5.142857143 = -5.142857143 8.428571429x + x2 = -5.142857143 The x term is 8.428571429x. Take half its coefficient (4.214285715). Square it (17.76020409) and add it to both sides. Add '17.76020409' to each side of the equation. 8.428571429x + 17.76020409 + x2 = -5.142857143 + 17.76020409 Reorder the terms: 17.76020409 + 8.428571429x + x2 = -5.142857143 + 17.76020409 Combine like terms: -5.142857143 + 17.76020409 = 12.617346947 17.76020409 + 8.428571429x + x2 = 12.617346947 Factor a perfect square on the left side: (x + 4.214285715)(x + 4.214285715) = 12.617346947 Calculate the square root of the right side: 3.552090504 Break this problem into two subproblems by setting (x + 4.214285715) equal to 3.552090504 and -3.552090504.Subproblem 1
x + 4.214285715 = 3.552090504 Simplifying x + 4.214285715 = 3.552090504 Reorder the terms: 4.214285715 + x = 3.552090504 Solving 4.214285715 + x = 3.552090504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.214285715' to each side of the equation. 4.214285715 + -4.214285715 + x = 3.552090504 + -4.214285715 Combine like terms: 4.214285715 + -4.214285715 = 0.000000000 0.000000000 + x = 3.552090504 + -4.214285715 x = 3.552090504 + -4.214285715 Combine like terms: 3.552090504 + -4.214285715 = -0.662195211 x = -0.662195211 Simplifying x = -0.662195211Subproblem 2
x + 4.214285715 = -3.552090504 Simplifying x + 4.214285715 = -3.552090504 Reorder the terms: 4.214285715 + x = -3.552090504 Solving 4.214285715 + x = -3.552090504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.214285715' to each side of the equation. 4.214285715 + -4.214285715 + x = -3.552090504 + -4.214285715 Combine like terms: 4.214285715 + -4.214285715 = 0.000000000 0.000000000 + x = -3.552090504 + -4.214285715 x = -3.552090504 + -4.214285715 Combine like terms: -3.552090504 + -4.214285715 = -7.766376219 x = -7.766376219 Simplifying x = -7.766376219Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.662195211, -7.766376219}Solution
x = {0, -0.662195211, -7.766376219}
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