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Simplifying 43 = 3(x + 1) * 2x Reorder the terms: 43 = 3(1 + x) * 2x Reorder the terms for easier multiplication: 43 = 3 * 2x(1 + x) Multiply 3 * 2 43 = 6x(1 + x) 43 = (1 * 6x + x * 6x) 43 = (6x + 6x2) Solving 43 = 6x + 6x2 Solving for variable 'x'. Reorder the terms: 43 + -6x + -6x2 = 6x + -6x + 6x2 + -6x2 Combine like terms: 6x + -6x = 0 43 + -6x + -6x2 = 0 + 6x2 + -6x2 43 + -6x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 43 + -6x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -7.166666667 + x + x2 = 0 Move the constant term to the right: Add '7.166666667' to each side of the equation. -7.166666667 + x + 7.166666667 + x2 = 0 + 7.166666667 Reorder the terms: -7.166666667 + 7.166666667 + x + x2 = 0 + 7.166666667 Combine like terms: -7.166666667 + 7.166666667 = 0.000000000 0.000000000 + x + x2 = 0 + 7.166666667 x + x2 = 0 + 7.166666667 Combine like terms: 0 + 7.166666667 = 7.166666667 x + x2 = 7.166666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 7.166666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 7.166666667 + 0.25 Combine like terms: 7.166666667 + 0.25 = 7.416666667 1.25 + x2 = 7.416666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7.416666667 Calculate the square root of the right side: 2.723355773 Break this problem into two subproblems by setting (x + 0.5) equal to 2.723355773 and -2.723355773.Subproblem 1
x + 0.5 = 2.723355773 Simplifying x + 0.5 = 2.723355773 Reorder the terms: 0.5 + x = 2.723355773 Solving 0.5 + x = 2.723355773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.723355773 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.723355773 + -0.5 x = 2.723355773 + -0.5 Combine like terms: 2.723355773 + -0.5 = 2.223355773 x = 2.223355773 Simplifying x = 2.223355773Subproblem 2
x + 0.5 = -2.723355773 Simplifying x + 0.5 = -2.723355773 Reorder the terms: 0.5 + x = -2.723355773 Solving 0.5 + x = -2.723355773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.723355773 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.723355773 + -0.5 x = -2.723355773 + -0.5 Combine like terms: -2.723355773 + -0.5 = -3.223355773 x = -3.223355773 Simplifying x = -3.223355773Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.223355773, -3.223355773}
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