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Simplifying 12x2 + -1x + -19 = 0 Reorder the terms: -19 + -1x + 12x2 = 0 Solving -19 + -1x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.583333333 + -0.08333333333x + x2 = 0 Move the constant term to the right: Add '1.583333333' to each side of the equation. -1.583333333 + -0.08333333333x + 1.583333333 + x2 = 0 + 1.583333333 Reorder the terms: -1.583333333 + 1.583333333 + -0.08333333333x + x2 = 0 + 1.583333333 Combine like terms: -1.583333333 + 1.583333333 = 0.000000000 0.000000000 + -0.08333333333x + x2 = 0 + 1.583333333 -0.08333333333x + x2 = 0 + 1.583333333 Combine like terms: 0 + 1.583333333 = 1.583333333 -0.08333333333x + x2 = 1.583333333 The x term is -0.08333333333x. Take half its coefficient (-0.04166666667). Square it (0.001736111111) and add it to both sides. Add '0.001736111111' to each side of the equation. -0.08333333333x + 0.001736111111 + x2 = 1.583333333 + 0.001736111111 Reorder the terms: 0.001736111111 + -0.08333333333x + x2 = 1.583333333 + 0.001736111111 Combine like terms: 1.583333333 + 0.001736111111 = 1.585069444111 0.001736111111 + -0.08333333333x + x2 = 1.585069444111 Factor a perfect square on the left side: (x + -0.04166666667)(x + -0.04166666667) = 1.585069444111 Calculate the square root of the right side: 1.258995411 Break this problem into two subproblems by setting (x + -0.04166666667) equal to 1.258995411 and -1.258995411.Subproblem 1
x + -0.04166666667 = 1.258995411 Simplifying x + -0.04166666667 = 1.258995411 Reorder the terms: -0.04166666667 + x = 1.258995411 Solving -0.04166666667 + x = 1.258995411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + x = 1.258995411 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = 1.258995411 + 0.04166666667 x = 1.258995411 + 0.04166666667 Combine like terms: 1.258995411 + 0.04166666667 = 1.30066207767 x = 1.30066207767 Simplifying x = 1.30066207767Subproblem 2
x + -0.04166666667 = -1.258995411 Simplifying x + -0.04166666667 = -1.258995411 Reorder the terms: -0.04166666667 + x = -1.258995411 Solving -0.04166666667 + x = -1.258995411 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + x = -1.258995411 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + x = -1.258995411 + 0.04166666667 x = -1.258995411 + 0.04166666667 Combine like terms: -1.258995411 + 0.04166666667 = -1.21732874433 x = -1.21732874433 Simplifying x = -1.21732874433Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.30066207767, -1.21732874433}
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