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Simplifying -5x2 + 24x + 27 = 0 Reorder the terms: 27 + 24x + -5x2 = 0 Solving 27 + 24x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -5.4 + -4.8x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + -4.8x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + -4.8x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + -4.8x + x2 = 0 + 5.4 -4.8x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 -4.8x + x2 = 5.4 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 = 5.4 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = 5.4 + 5.76 Combine like terms: 5.4 + 5.76 = 11.16 5.76 + -4.8x + x2 = 11.16 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 11.16 Calculate the square root of the right side: 3.340658618 Break this problem into two subproblems by setting (x + -2.4) equal to 3.340658618 and -3.340658618.Subproblem 1
x + -2.4 = 3.340658618 Simplifying x + -2.4 = 3.340658618 Reorder the terms: -2.4 + x = 3.340658618 Solving -2.4 + x = 3.340658618 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 = 3.340658618 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 3.340658618 + 2.4 x = 3.340658618 + 2.4 Combine like terms: 3.340658618 + 2.4 = 5.740658618 x = 5.740658618 Simplifying x = 5.740658618Subproblem 2
x + -2.4 = -3.340658618 Simplifying x + -2.4 = -3.340658618 Reorder the terms: -2.4 + x = -3.340658618 Solving -2.4 + x = -3.340658618 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 = -3.340658618 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -3.340658618 + 2.4 x = -3.340658618 + 2.4 Combine like terms: -3.340658618 + 2.4 = -0.940658618 x = -0.940658618 Simplifying x = -0.940658618Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.740658618, -0.940658618}
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