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Simplifying 4x2 + -13x + -45 = 0 Reorder the terms: -45 + -13x + 4x2 = 0 Solving -45 + -13x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -11.25 + -3.25x + x2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + -3.25x + 11.25 + x2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + -3.25x + x2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + -3.25x + x2 = 0 + 11.25 -3.25x + x2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 -3.25x + x2 = 11.25 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 11.25 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 11.25 + 2.640625 Combine like terms: 11.25 + 2.640625 = 13.890625 2.640625 + -3.25x + x2 = 13.890625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 13.890625 Calculate the square root of the right side: 3.727012879 Break this problem into two subproblems by setting (x + -1.625) equal to 3.727012879 and -3.727012879.Subproblem 1
x + -1.625 = 3.727012879 Simplifying x + -1.625 = 3.727012879 Reorder the terms: -1.625 + x = 3.727012879 Solving -1.625 + x = 3.727012879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 3.727012879 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 3.727012879 + 1.625 x = 3.727012879 + 1.625 Combine like terms: 3.727012879 + 1.625 = 5.352012879 x = 5.352012879 Simplifying x = 5.352012879Subproblem 2
x + -1.625 = -3.727012879 Simplifying x + -1.625 = -3.727012879 Reorder the terms: -1.625 + x = -3.727012879 Solving -1.625 + x = -3.727012879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -3.727012879 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -3.727012879 + 1.625 x = -3.727012879 + 1.625 Combine like terms: -3.727012879 + 1.625 = -2.102012879 x = -2.102012879 Simplifying x = -2.102012879Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.352012879, -2.102012879}
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