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Simplifying 3(x + 4) * 2x + -5 = 0 Reorder the terms: 3(4 + x) * 2x + -5 = 0 Reorder the terms for easier multiplication: 3 * 2x(4 + x) + -5 = 0 Multiply 3 * 2 6x(4 + x) + -5 = 0 (4 * 6x + x * 6x) + -5 = 0 (24x + 6x2) + -5 = 0 Reorder the terms: -5 + 24x + 6x2 = 0 Solving -5 + 24x + 6x2 = 0 Solving for variable 'x'. 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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