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Simplifying 0.03x2 + -1.2x + 13 = 7x Reorder the terms: 13 + -1.2x + 0.03x2 = 7x Solving 13 + -1.2x + 0.03x2 = 7x Solving for variable 'x'. Reorder the terms: 13 + -1.2x + -7x + 0.03x2 = 7x + -7x Combine like terms: -1.2x + -7x = -8.2x 13 + -8.2x + 0.03x2 = 7x + -7x Combine like terms: 7x + -7x = 0 13 + -8.2x + 0.03x2 = 0 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. 433.3333333 + -273.3333333x + x2 = 0 Move the constant term to the right: Add '-433.3333333' to each side of the equation. 433.3333333 + -273.3333333x + -433.3333333 + x2 = 0 + -433.3333333 Reorder the terms: 433.3333333 + -433.3333333 + -273.3333333x + x2 = 0 + -433.3333333 Combine like terms: 433.3333333 + -433.3333333 = 0.0000000 0.0000000 + -273.3333333x + x2 = 0 + -433.3333333 -273.3333333x + x2 = 0 + -433.3333333 Combine like terms: 0 + -433.3333333 = -433.3333333 -273.3333333x + x2 = -433.3333333 The x term is -273.3333333x. Take half its coefficient (-136.6666667). Square it (18677.77779) and add it to both sides. Add '18677.77779' to each side of the equation. -273.3333333x + 18677.77779 + x2 = -433.3333333 + 18677.77779 Reorder the terms: 18677.77779 + -273.3333333x + x2 = -433.3333333 + 18677.77779 Combine like terms: -433.3333333 + 18677.77779 = 18244.4444567 18677.77779 + -273.3333333x + x2 = 18244.4444567 Factor a perfect square on the left side: (x + -136.6666667)(x + -136.6666667) = 18244.4444567 Calculate the square root of the right side: 135.071997308 Break this problem into two subproblems by setting (x + -136.6666667) equal to 135.071997308 and -135.071997308.Subproblem 1
x + -136.6666667 = 135.071997308 Simplifying x + -136.6666667 = 135.071997308 Reorder the terms: -136.6666667 + x = 135.071997308 Solving -136.6666667 + x = 135.071997308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '136.6666667' to each side of the equation. -136.6666667 + 136.6666667 + x = 135.071997308 + 136.6666667 Combine like terms: -136.6666667 + 136.6666667 = 0.0000000 0.0000000 + x = 135.071997308 + 136.6666667 x = 135.071997308 + 136.6666667 Combine like terms: 135.071997308 + 136.6666667 = 271.738664008 x = 271.738664008 Simplifying x = 271.738664008Subproblem 2
x + -136.6666667 = -135.071997308 Simplifying x + -136.6666667 = -135.071997308 Reorder the terms: -136.6666667 + x = -135.071997308 Solving -136.6666667 + x = -135.071997308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '136.6666667' to each side of the equation. -136.6666667 + 136.6666667 + x = -135.071997308 + 136.6666667 Combine like terms: -136.6666667 + 136.6666667 = 0.0000000 0.0000000 + x = -135.071997308 + 136.6666667 x = -135.071997308 + 136.6666667 Combine like terms: -135.071997308 + 136.6666667 = 1.594669392 x = 1.594669392 Simplifying x = 1.594669392Solution
The solution to the problem is based on the solutions from the subproblems. x = {271.738664008, 1.594669392}
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