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Simplifying 36x2 + -6x + -7 = 0 Reorder the terms: -7 + -6x + 36x2 = 0 Solving -7 + -6x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.1944444444 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.1944444444' to each side of the equation. -0.1944444444 + -0.1666666667x + 0.1944444444 + x2 = 0 + 0.1944444444 Reorder the terms: -0.1944444444 + 0.1944444444 + -0.1666666667x + x2 = 0 + 0.1944444444 Combine like terms: -0.1944444444 + 0.1944444444 = 0.0000000000 0.0000000000 + -0.1666666667x + x2 = 0 + 0.1944444444 -0.1666666667x + x2 = 0 + 0.1944444444 Combine like terms: 0 + 0.1944444444 = 0.1944444444 -0.1666666667x + x2 = 0.1944444444 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 0.1944444444 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 0.1944444444 + 0.006944444447 Combine like terms: 0.1944444444 + 0.006944444447 = 0.201388888847 0.006944444447 + -0.1666666667x + x2 = 0.201388888847 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 0.201388888847 Calculate the square root of the right side: 0.448763734 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 0.448763734 and -0.448763734.Subproblem 1
x + -0.08333333335 = 0.448763734 Simplifying x + -0.08333333335 = 0.448763734 Reorder the terms: -0.08333333335 + x = 0.448763734 Solving -0.08333333335 + x = 0.448763734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 0.448763734 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 0.448763734 + 0.08333333335 x = 0.448763734 + 0.08333333335 Combine like terms: 0.448763734 + 0.08333333335 = 0.53209706735 x = 0.53209706735 Simplifying x = 0.53209706735Subproblem 2
x + -0.08333333335 = -0.448763734 Simplifying x + -0.08333333335 = -0.448763734 Reorder the terms: -0.08333333335 + x = -0.448763734 Solving -0.08333333335 + x = -0.448763734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -0.448763734 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -0.448763734 + 0.08333333335 x = -0.448763734 + 0.08333333335 Combine like terms: -0.448763734 + 0.08333333335 = -0.36543040065 x = -0.36543040065 Simplifying x = -0.36543040065Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.53209706735, -0.36543040065}
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