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Simplifying 3x(x + 4) + 5 = 28 Reorder the terms: 3x(4 + x) + 5 = 28 (4 * 3x + x * 3x) + 5 = 28 (12x + 3x2) + 5 = 28 Reorder the terms: 5 + 12x + 3x2 = 28 Solving 5 + 12x + 3x2 = 28 Solving for variable 'x'. Reorder the terms: 5 + -28 + 12x + 3x2 = 28 + -28 Combine like terms: 5 + -28 = -23 -23 + 12x + 3x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -23 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7.666666667 + 4x + x2 = 0 Move the constant term to the right: Add '7.666666667' to each side of the equation. -7.666666667 + 4x + 7.666666667 + x2 = 0 + 7.666666667 Reorder the terms: -7.666666667 + 7.666666667 + 4x + x2 = 0 + 7.666666667 Combine like terms: -7.666666667 + 7.666666667 = 0.000000000 0.000000000 + 4x + x2 = 0 + 7.666666667 4x + x2 = 0 + 7.666666667 Combine like terms: 0 + 7.666666667 = 7.666666667 4x + x2 = 7.666666667 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 7.666666667 + 4 Reorder the terms: 4 + 4x + x2 = 7.666666667 + 4 Combine like terms: 7.666666667 + 4 = 11.666666667 4 + 4x + x2 = 11.666666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 11.666666667 Calculate the square root of the right side: 3.415650255 Break this problem into two subproblems by setting (x + 2) equal to 3.415650255 and -3.415650255.Subproblem 1
x + 2 = 3.415650255 Simplifying x + 2 = 3.415650255 Reorder the terms: 2 + x = 3.415650255 Solving 2 + x = 3.415650255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.415650255 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.415650255 + -2 x = 3.415650255 + -2 Combine like terms: 3.415650255 + -2 = 1.415650255 x = 1.415650255 Simplifying x = 1.415650255Subproblem 2
x + 2 = -3.415650255 Simplifying x + 2 = -3.415650255 Reorder the terms: 2 + x = -3.415650255 Solving 2 + x = -3.415650255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.415650255 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.415650255 + -2 x = -3.415650255 + -2 Combine like terms: -3.415650255 + -2 = -5.415650255 x = -5.415650255 Simplifying x = -5.415650255Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.415650255, -5.415650255}
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