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Simplifying 42x2 + -480x + -2463 = 0 Reorder the terms: -2463 + -480x + 42x2 = 0 Solving -2463 + -480x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-821 + -160x + 14x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-821 + -160x + 14x2)' equal to zero and attempt to solve: Simplifying -821 + -160x + 14x2 = 0 Solving -821 + -160x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -58.64285714 + -11.42857143x + x2 = 0 Move the constant term to the right: Add '58.64285714' to each side of the equation. -58.64285714 + -11.42857143x + 58.64285714 + x2 = 0 + 58.64285714 Reorder the terms: -58.64285714 + 58.64285714 + -11.42857143x + x2 = 0 + 58.64285714 Combine like terms: -58.64285714 + 58.64285714 = 0.00000000 0.00000000 + -11.42857143x + x2 = 0 + 58.64285714 -11.42857143x + x2 = 0 + 58.64285714 Combine like terms: 0 + 58.64285714 = 58.64285714 -11.42857143x + x2 = 58.64285714 The x term is -11.42857143x. Take half its coefficient (-5.714285715). Square it (32.65306123) and add it to both sides. Add '32.65306123' to each side of the equation. -11.42857143x + 32.65306123 + x2 = 58.64285714 + 32.65306123 Reorder the terms: 32.65306123 + -11.42857143x + x2 = 58.64285714 + 32.65306123 Combine like terms: 58.64285714 + 32.65306123 = 91.29591837 32.65306123 + -11.42857143x + x2 = 91.29591837 Factor a perfect square on the left side: (x + -5.714285715)(x + -5.714285715) = 91.29591837 Calculate the square root of the right side: 9.554889762 Break this problem into two subproblems by setting (x + -5.714285715) equal to 9.554889762 and -9.554889762.Subproblem 1
x + -5.714285715 = 9.554889762 Simplifying x + -5.714285715 = 9.554889762 Reorder the terms: -5.714285715 + x = 9.554889762 Solving -5.714285715 + x = 9.554889762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.714285715' to each side of the equation. -5.714285715 + 5.714285715 + x = 9.554889762 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + x = 9.554889762 + 5.714285715 x = 9.554889762 + 5.714285715 Combine like terms: 9.554889762 + 5.714285715 = 15.269175477 x = 15.269175477 Simplifying x = 15.269175477Subproblem 2
x + -5.714285715 = -9.554889762 Simplifying x + -5.714285715 = -9.554889762 Reorder the terms: -5.714285715 + x = -9.554889762 Solving -5.714285715 + x = -9.554889762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.714285715' to each side of the equation. -5.714285715 + 5.714285715 + x = -9.554889762 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + x = -9.554889762 + 5.714285715 x = -9.554889762 + 5.714285715 Combine like terms: -9.554889762 + 5.714285715 = -3.840604047 x = -3.840604047 Simplifying x = -3.840604047Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.269175477, -3.840604047}Solution
x = {15.269175477, -3.840604047}
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