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Simplifying 3x(x + -4)(x + 2) = 3x3 + -5 Reorder the terms: 3x(-4 + x)(x + 2) = 3x3 + -5 Reorder the terms: 3x(-4 + x)(2 + x) = 3x3 + -5 Multiply (-4 + x) * (2 + x) 3x(-4(2 + x) + x(2 + x)) = 3x3 + -5 3x((2 * -4 + x * -4) + x(2 + x)) = 3x3 + -5 3x((-8 + -4x) + x(2 + x)) = 3x3 + -5 3x(-8 + -4x + (2 * x + x * x)) = 3x3 + -5 3x(-8 + -4x + (2x + x2)) = 3x3 + -5 Combine like terms: -4x + 2x = -2x 3x(-8 + -2x + x2) = 3x3 + -5 (-8 * 3x + -2x * 3x + x2 * 3x) = 3x3 + -5 (-24x + -6x2 + 3x3) = 3x3 + -5 Reorder the terms: -24x + -6x2 + 3x3 = -5 + 3x3 Add '-3x3' to each side of the equation. -24x + -6x2 + 3x3 + -3x3 = -5 + 3x3 + -3x3 Combine like terms: 3x3 + -3x3 = 0 -24x + -6x2 + 0 = -5 + 3x3 + -3x3 -24x + -6x2 = -5 + 3x3 + -3x3 Combine like terms: 3x3 + -3x3 = 0 -24x + -6x2 = -5 + 0 -24x + -6x2 = -5 Solving -24x + -6x2 = -5 Solving for variable 'x'. Reorder the terms: 5 + -24x + -6x2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + -24x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.8333333333 + 4x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 4x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 4x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 4x + x2 = 0 + 0.8333333333 4x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 4x + x2 = 0.8333333333 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 = 0.8333333333 + 4 Reorder the terms: 4 + 4x + x2 = 0.8333333333 + 4 Combine like terms: 0.8333333333 + 4 = 4.8333333333 4 + 4x + x2 = 4.8333333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 4.8333333333 Calculate the square root of the right side: 2.198484326 Break this problem into two subproblems by setting (x + 2) equal to 2.198484326 and -2.198484326.Subproblem 1
x + 2 = 2.198484326 Simplifying x + 2 = 2.198484326 Reorder the terms: 2 + x = 2.198484326 Solving 2 + x = 2.198484326 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 = 2.198484326 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.198484326 + -2 x = 2.198484326 + -2 Combine like terms: 2.198484326 + -2 = 0.198484326 x = 0.198484326 Simplifying x = 0.198484326Subproblem 2
x + 2 = -2.198484326 Simplifying x + 2 = -2.198484326 Reorder the terms: 2 + x = -2.198484326 Solving 2 + x = -2.198484326 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 = -2.198484326 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.198484326 + -2 x = -2.198484326 + -2 Combine like terms: -2.198484326 + -2 = -4.198484326 x = -4.198484326 Simplifying x = -4.198484326Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.198484326, -4.198484326}
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