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Simplifying 3x + 46 = 4x(x + 6) Reorder the terms: 46 + 3x = 4x(x + 6) Reorder the terms: 46 + 3x = 4x(6 + x) 46 + 3x = (6 * 4x + x * 4x) 46 + 3x = (24x + 4x2) Solving 46 + 3x = 24x + 4x2 Solving for variable 'x'. Combine like terms: 3x + -24x = -21x 46 + -21x + -4x2 = 24x + 4x2 + -24x + -4x2 Reorder the terms: 46 + -21x + -4x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 46 + -21x + -4x2 = 0 + 4x2 + -4x2 46 + -21x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 46 + -21x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -11.5 + 5.25x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + 5.25x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + 5.25x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + 5.25x + x2 = 0 + 11.5 5.25x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 5.25x + x2 = 11.5 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = 11.5 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = 11.5 + 6.890625 Combine like terms: 11.5 + 6.890625 = 18.390625 6.890625 + 5.25x + x2 = 18.390625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 18.390625 Calculate the square root of the right side: 4.2884292 Break this problem into two subproblems by setting (x + 2.625) equal to 4.2884292 and -4.2884292.Subproblem 1
x + 2.625 = 4.2884292 Simplifying x + 2.625 = 4.2884292 Reorder the terms: 2.625 + x = 4.2884292 Solving 2.625 + x = 4.2884292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 4.2884292 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 4.2884292 + -2.625 x = 4.2884292 + -2.625 Combine like terms: 4.2884292 + -2.625 = 1.6634292 x = 1.6634292 Simplifying x = 1.6634292Subproblem 2
x + 2.625 = -4.2884292 Simplifying x + 2.625 = -4.2884292 Reorder the terms: 2.625 + x = -4.2884292 Solving 2.625 + x = -4.2884292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -4.2884292 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -4.2884292 + -2.625 x = -4.2884292 + -2.625 Combine like terms: -4.2884292 + -2.625 = -6.9134292 x = -6.9134292 Simplifying x = -6.9134292Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6634292, -6.9134292}
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