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Simplifying (3x4) + -1(37x2) + 10 = 0 Remove parenthesis around (37x2) (3x4) + -1 * 37x2 + 10 = 0 Multiply -1 * 37 (3x4) + -37x2 + 10 = 0 Reorder the terms: 10 + -37x2 + (3x4) = 0 Solving 10 + -37x2 + (3x4) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + -12.33333333x2 + x4 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -12.33333333x2 + -3.333333333 + x4 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -12.33333333x2 + x4 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -12.33333333x2 + x4 = 0 + -3.333333333 -12.33333333x2 + x4 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -12.33333333x2 + x4 = -3.333333333 The x term is -12.33333333x2. Take half its coefficient (-6.166666665). Square it (38.02777776) and add it to both sides. Add '38.02777776' to each side of the equation. -12.33333333x2 + 38.02777776 + x4 = -3.333333333 + 38.02777776 Reorder the terms: 38.02777776 + -12.33333333x2 + x4 = -3.333333333 + 38.02777776 Combine like terms: -3.333333333 + 38.02777776 = 34.694444427 38.02777776 + -12.33333333x2 + x4 = 34.694444427 Factor a perfect square on the left side: ((x2) + -6.166666665)((x2) + -6.166666665) = 34.694444427 Calculate the square root of the right side: 5.890199014 Break this problem into two subproblems by setting ((x2) + -6.166666665) equal to 5.890199014 and -5.890199014.Subproblem 1
(x2) + -6.166666665 = 5.890199014 Simplifying (x2) + -6.166666665 = 5.890199014 x2 + -6.166666665 = 5.890199014 Reorder the terms: -6.166666665 + x2 = 5.890199014 Solving -6.166666665 + x2 = 5.890199014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + x2 = 5.890199014 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + x2 = 5.890199014 + 6.166666665 x2 = 5.890199014 + 6.166666665 Combine like terms: 5.890199014 + 6.166666665 = 12.056865679 x2 = 12.056865679 Simplifying x2 = 12.056865679 Take the square root of each side: x = {-3.472299768, 3.472299768}Subproblem 2
(x2) + -6.166666665 = -5.890199014 Simplifying (x2) + -6.166666665 = -5.890199014 x2 + -6.166666665 = -5.890199014 Reorder the terms: -6.166666665 + x2 = -5.890199014 Solving -6.166666665 + x2 = -5.890199014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + x2 = -5.890199014 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + x2 = -5.890199014 + 6.166666665 x2 = -5.890199014 + 6.166666665 Combine like terms: -5.890199014 + 6.166666665 = 0.276467651 x2 = 0.276467651 Simplifying x2 = 0.276467651 Take the square root of each side: x = {-0.525801912, 0.525801912}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.472299768, 3.472299768, -0.525801912, 0.525801912}
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