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Simplifying x(20x + -27) = 54 Reorder the terms: x(-27 + 20x) = 54 (-27 * x + 20x * x) = 54 (-27x + 20x2) = 54 Solving -27x + 20x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + -27x + 20x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + -27x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -2.7 + -1.35x + x2 = 0 Move the constant term to the right: Add '2.7' to each side of the equation. -2.7 + -1.35x + 2.7 + x2 = 0 + 2.7 Reorder the terms: -2.7 + 2.7 + -1.35x + x2 = 0 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + -1.35x + x2 = 0 + 2.7 -1.35x + x2 = 0 + 2.7 Combine like terms: 0 + 2.7 = 2.7 -1.35x + x2 = 2.7 The x term is -1.35x. Take half its coefficient (-0.675). Square it (0.455625) and add it to both sides. Add '0.455625' to each side of the equation. -1.35x + 0.455625 + x2 = 2.7 + 0.455625 Reorder the terms: 0.455625 + -1.35x + x2 = 2.7 + 0.455625 Combine like terms: 2.7 + 0.455625 = 3.155625 0.455625 + -1.35x + x2 = 3.155625 Factor a perfect square on the left side: (x + -0.675)(x + -0.675) = 3.155625 Calculate the square root of the right side: 1.776407892 Break this problem into two subproblems by setting (x + -0.675) equal to 1.776407892 and -1.776407892.Subproblem 1
x + -0.675 = 1.776407892 Simplifying x + -0.675 = 1.776407892 Reorder the terms: -0.675 + x = 1.776407892 Solving -0.675 + x = 1.776407892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.675' to each side of the equation. -0.675 + 0.675 + x = 1.776407892 + 0.675 Combine like terms: -0.675 + 0.675 = 0.000 0.000 + x = 1.776407892 + 0.675 x = 1.776407892 + 0.675 Combine like terms: 1.776407892 + 0.675 = 2.451407892 x = 2.451407892 Simplifying x = 2.451407892Subproblem 2
x + -0.675 = -1.776407892 Simplifying x + -0.675 = -1.776407892 Reorder the terms: -0.675 + x = -1.776407892 Solving -0.675 + x = -1.776407892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.675' to each side of the equation. -0.675 + 0.675 + x = -1.776407892 + 0.675 Combine like terms: -0.675 + 0.675 = 0.000 0.000 + x = -1.776407892 + 0.675 x = -1.776407892 + 0.675 Combine like terms: -1.776407892 + 0.675 = -1.101407892 x = -1.101407892 Simplifying x = -1.101407892Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.451407892, -1.101407892}
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