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Simplifying 42x2 + -480x + -2465 = 0 Reorder the terms: -2465 + -480x + 42x2 = 0 Solving -2465 + -480x + 42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -58.69047619 + -11.42857143x + x2 = 0 Move the constant term to the right: Add '58.69047619' to each side of the equation. -58.69047619 + -11.42857143x + 58.69047619 + x2 = 0 + 58.69047619 Reorder the terms: -58.69047619 + 58.69047619 + -11.42857143x + x2 = 0 + 58.69047619 Combine like terms: -58.69047619 + 58.69047619 = 0.00000000 0.00000000 + -11.42857143x + x2 = 0 + 58.69047619 -11.42857143x + x2 = 0 + 58.69047619 Combine like terms: 0 + 58.69047619 = 58.69047619 -11.42857143x + x2 = 58.69047619 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 = 58.69047619 + 32.65306123 Reorder the terms: 32.65306123 + -11.42857143x + x2 = 58.69047619 + 32.65306123 Combine like terms: 58.69047619 + 32.65306123 = 91.34353742 32.65306123 + -11.42857143x + x2 = 91.34353742 Factor a perfect square on the left side: (x + -5.714285715)(x + -5.714285715) = 91.34353742 Calculate the square root of the right side: 9.557381306 Break this problem into two subproblems by setting (x + -5.714285715) equal to 9.557381306 and -9.557381306.Subproblem 1
x + -5.714285715 = 9.557381306 Simplifying x + -5.714285715 = 9.557381306 Reorder the terms: -5.714285715 + x = 9.557381306 Solving -5.714285715 + x = 9.557381306 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 = 9.557381306 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + x = 9.557381306 + 5.714285715 x = 9.557381306 + 5.714285715 Combine like terms: 9.557381306 + 5.714285715 = 15.271667021 x = 15.271667021 Simplifying x = 15.271667021Subproblem 2
x + -5.714285715 = -9.557381306 Simplifying x + -5.714285715 = -9.557381306 Reorder the terms: -5.714285715 + x = -9.557381306 Solving -5.714285715 + x = -9.557381306 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 = -9.557381306 + 5.714285715 Combine like terms: -5.714285715 + 5.714285715 = 0.000000000 0.000000000 + x = -9.557381306 + 5.714285715 x = -9.557381306 + 5.714285715 Combine like terms: -9.557381306 + 5.714285715 = -3.843095591 x = -3.843095591 Simplifying x = -3.843095591Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.271667021, -3.843095591}
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