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Simplifying 6x2 + -1x + -3 = 102 Reorder the terms: -3 + -1x + 6x2 = 102 Solving -3 + -1x + 6x2 = 102 Solving for variable 'x'. Reorder the terms: -3 + -102 + -1x + 6x2 = 102 + -102 Combine like terms: -3 + -102 = -105 -105 + -1x + 6x2 = 102 + -102 Combine like terms: 102 + -102 = 0 -105 + -1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -17.5 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -0.1666666667x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -0.1666666667x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -0.1666666667x + x2 = 0 + 17.5 -0.1666666667x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -0.1666666667x + x2 = 17.5 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 = 17.5 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 17.5 + 0.006944444447 Combine like terms: 17.5 + 0.006944444447 = 17.506944444447 0.006944444447 + -0.1666666667x + x2 = 17.506944444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 17.506944444447 Calculate the square root of the right side: 4.18413007 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 4.18413007 and -4.18413007.Subproblem 1
x + -0.08333333335 = 4.18413007 Simplifying x + -0.08333333335 = 4.18413007 Reorder the terms: -0.08333333335 + x = 4.18413007 Solving -0.08333333335 + x = 4.18413007 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 = 4.18413007 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 4.18413007 + 0.08333333335 x = 4.18413007 + 0.08333333335 Combine like terms: 4.18413007 + 0.08333333335 = 4.26746340335 x = 4.26746340335 Simplifying x = 4.26746340335Subproblem 2
x + -0.08333333335 = -4.18413007 Simplifying x + -0.08333333335 = -4.18413007 Reorder the terms: -0.08333333335 + x = -4.18413007 Solving -0.08333333335 + x = -4.18413007 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 = -4.18413007 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -4.18413007 + 0.08333333335 x = -4.18413007 + 0.08333333335 Combine like terms: -4.18413007 + 0.08333333335 = -4.10079673665 x = -4.10079673665 Simplifying x = -4.10079673665Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.26746340335, -4.10079673665}
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