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Simplifying 42x2 + -478x + -2459 = 0 Reorder the terms: -2459 + -478x + 42x2 = 0 Solving -2459 + -478x + 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'. -58.54761905 + -11.38095238x + x2 = 0 Move the constant term to the right: Add '58.54761905' to each side of the equation. -58.54761905 + -11.38095238x + 58.54761905 + x2 = 0 + 58.54761905 Reorder the terms: -58.54761905 + 58.54761905 + -11.38095238x + x2 = 0 + 58.54761905 Combine like terms: -58.54761905 + 58.54761905 = 0.00000000 0.00000000 + -11.38095238x + x2 = 0 + 58.54761905 -11.38095238x + x2 = 0 + 58.54761905 Combine like terms: 0 + 58.54761905 = 58.54761905 -11.38095238x + x2 = 58.54761905 The x term is -11.38095238x. Take half its coefficient (-5.69047619). Square it (32.38151927) and add it to both sides. Add '32.38151927' to each side of the equation. -11.38095238x + 32.38151927 + x2 = 58.54761905 + 32.38151927 Reorder the terms: 32.38151927 + -11.38095238x + x2 = 58.54761905 + 32.38151927 Combine like terms: 58.54761905 + 32.38151927 = 90.92913832 32.38151927 + -11.38095238x + x2 = 90.92913832 Factor a perfect square on the left side: (x + -5.69047619)(x + -5.69047619) = 90.92913832 Calculate the square root of the right side: 9.53567713 Break this problem into two subproblems by setting (x + -5.69047619) equal to 9.53567713 and -9.53567713.Subproblem 1
x + -5.69047619 = 9.53567713 Simplifying x + -5.69047619 = 9.53567713 Reorder the terms: -5.69047619 + x = 9.53567713 Solving -5.69047619 + x = 9.53567713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.69047619' to each side of the equation. -5.69047619 + 5.69047619 + x = 9.53567713 + 5.69047619 Combine like terms: -5.69047619 + 5.69047619 = 0.00000000 0.00000000 + x = 9.53567713 + 5.69047619 x = 9.53567713 + 5.69047619 Combine like terms: 9.53567713 + 5.69047619 = 15.22615332 x = 15.22615332 Simplifying x = 15.22615332Subproblem 2
x + -5.69047619 = -9.53567713 Simplifying x + -5.69047619 = -9.53567713 Reorder the terms: -5.69047619 + x = -9.53567713 Solving -5.69047619 + x = -9.53567713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.69047619' to each side of the equation. -5.69047619 + 5.69047619 + x = -9.53567713 + 5.69047619 Combine like terms: -5.69047619 + 5.69047619 = 0.00000000 0.00000000 + x = -9.53567713 + 5.69047619 x = -9.53567713 + 5.69047619 Combine like terms: -9.53567713 + 5.69047619 = -3.84520094 x = -3.84520094 Simplifying x = -3.84520094Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.22615332, -3.84520094}
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