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Simplifying -5x2 + 24x + 54 = 21 Reorder the terms: 54 + 24x + -5x2 = 21 Solving 54 + 24x + -5x2 = 21 Solving for variable 'x'. Reorder the terms: 54 + -21 + 24x + -5x2 = 21 + -21 Combine like terms: 54 + -21 = 33 33 + 24x + -5x2 = 21 + -21 Combine like terms: 21 + -21 = 0 33 + 24x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -6.6 + -4.8x + x2 = 0 Move the constant term to the right: Add '6.6' to each side of the equation. -6.6 + -4.8x + 6.6 + x2 = 0 + 6.6 Reorder the terms: -6.6 + 6.6 + -4.8x + x2 = 0 + 6.6 Combine like terms: -6.6 + 6.6 = 0.0 0.0 + -4.8x + x2 = 0 + 6.6 -4.8x + x2 = 0 + 6.6 Combine like terms: 0 + 6.6 = 6.6 -4.8x + x2 = 6.6 The x term is -4.8x. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8x + 5.76 + x2 = 6.6 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = 6.6 + 5.76 Combine like terms: 6.6 + 5.76 = 12.36 5.76 + -4.8x + x2 = 12.36 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 12.36 Calculate the square root of the right side: 3.515679166 Break this problem into two subproblems by setting (x + -2.4) equal to 3.515679166 and -3.515679166.Subproblem 1
x + -2.4 = 3.515679166 Simplifying x + -2.4 = 3.515679166 Reorder the terms: -2.4 + x = 3.515679166 Solving -2.4 + x = 3.515679166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = 3.515679166 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 3.515679166 + 2.4 x = 3.515679166 + 2.4 Combine like terms: 3.515679166 + 2.4 = 5.915679166 x = 5.915679166 Simplifying x = 5.915679166Subproblem 2
x + -2.4 = -3.515679166 Simplifying x + -2.4 = -3.515679166 Reorder the terms: -2.4 + x = -3.515679166 Solving -2.4 + x = -3.515679166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = -3.515679166 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -3.515679166 + 2.4 x = -3.515679166 + 2.4 Combine like terms: -3.515679166 + 2.4 = -1.115679166 x = -1.115679166 Simplifying x = -1.115679166Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.915679166, -1.115679166}
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