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Simplifying 4x2 + -54 + 5x = 0 Reorder the terms: -54 + 5x + 4x2 = 0 Solving -54 + 5x + 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'. -13.5 + 1.25x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 1.25x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 1.25x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 1.25x + x2 = 0 + 13.5 1.25x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 1.25x + x2 = 13.5 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 13.5 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 13.5 + 0.390625 Combine like terms: 13.5 + 0.390625 = 13.890625 0.390625 + 1.25x + x2 = 13.890625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 13.890625 Calculate the square root of the right side: 3.727012879 Break this problem into two subproblems by setting (x + 0.625) equal to 3.727012879 and -3.727012879.Subproblem 1
x + 0.625 = 3.727012879 Simplifying x + 0.625 = 3.727012879 Reorder the terms: 0.625 + x = 3.727012879 Solving 0.625 + x = 3.727012879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 3.727012879 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 3.727012879 + -0.625 x = 3.727012879 + -0.625 Combine like terms: 3.727012879 + -0.625 = 3.102012879 x = 3.102012879 Simplifying x = 3.102012879Subproblem 2
x + 0.625 = -3.727012879 Simplifying x + 0.625 = -3.727012879 Reorder the terms: 0.625 + x = -3.727012879 Solving 0.625 + x = -3.727012879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -3.727012879 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -3.727012879 + -0.625 x = -3.727012879 + -0.625 Combine like terms: -3.727012879 + -0.625 = -4.352012879 x = -4.352012879 Simplifying x = -4.352012879Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.102012879, -4.352012879}
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