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Simplifying 6x + 54 = x2 + 4x2 Reorder the terms: 54 + 6x = x2 + 4x2 Combine like terms: x2 + 4x2 = 5x2 54 + 6x = 5x2 Solving 54 + 6x = 5x2 Solving for variable 'x'. Combine like terms: 5x2 + -5x2 = 0 54 + 6x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -10.8 + -1.2x + x2 = 0 Move the constant term to the right: Add '10.8' to each side of the equation. -10.8 + -1.2x + 10.8 + x2 = 0 + 10.8 Reorder the terms: -10.8 + 10.8 + -1.2x + x2 = 0 + 10.8 Combine like terms: -10.8 + 10.8 = 0.0 0.0 + -1.2x + x2 = 0 + 10.8 -1.2x + x2 = 0 + 10.8 Combine like terms: 0 + 10.8 = 10.8 -1.2x + x2 = 10.8 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 10.8 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 10.8 + 0.36 Combine like terms: 10.8 + 0.36 = 11.16 0.36 + -1.2x + x2 = 11.16 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 11.16 Calculate the square root of the right side: 3.340658618 Break this problem into two subproblems by setting (x + -0.6) equal to 3.340658618 and -3.340658618.Subproblem 1
x + -0.6 = 3.340658618 Simplifying x + -0.6 = 3.340658618 Reorder the terms: -0.6 + x = 3.340658618 Solving -0.6 + x = 3.340658618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 3.340658618 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 3.340658618 + 0.6 x = 3.340658618 + 0.6 Combine like terms: 3.340658618 + 0.6 = 3.940658618 x = 3.940658618 Simplifying x = 3.940658618Subproblem 2
x + -0.6 = -3.340658618 Simplifying x + -0.6 = -3.340658618 Reorder the terms: -0.6 + x = -3.340658618 Solving -0.6 + x = -3.340658618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -3.340658618 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -3.340658618 + 0.6 x = -3.340658618 + 0.6 Combine like terms: -3.340658618 + 0.6 = -2.740658618 x = -2.740658618 Simplifying x = -2.740658618Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.940658618, -2.740658618}
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