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Simplifying 3(x + 1) * 2x = 53 Reorder the terms: 3(1 + x) * 2x = 53 Reorder the terms for easier multiplication: 3 * 2x(1 + x) = 53 Multiply 3 * 2 6x(1 + x) = 53 (1 * 6x + x * 6x) = 53 (6x + 6x2) = 53 Solving 6x + 6x2 = 53 Solving for variable 'x'. Reorder the terms: -53 + 6x + 6x2 = 53 + -53 Combine like terms: 53 + -53 = 0 -53 + 6x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -8.833333333 + x + x2 = 0 Move the constant term to the right: Add '8.833333333' to each side of the equation. -8.833333333 + x + 8.833333333 + x2 = 0 + 8.833333333 Reorder the terms: -8.833333333 + 8.833333333 + x + x2 = 0 + 8.833333333 Combine like terms: -8.833333333 + 8.833333333 = 0.000000000 0.000000000 + x + x2 = 0 + 8.833333333 x + x2 = 0 + 8.833333333 Combine like terms: 0 + 8.833333333 = 8.833333333 x + x2 = 8.833333333 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 = 8.833333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 8.833333333 + 0.25 Combine like terms: 8.833333333 + 0.25 = 9.083333333 1.25 + x2 = 9.083333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 9.083333333 Calculate the square root of the right side: 3.013856887 Break this problem into two subproblems by setting (x + 0.5) equal to 3.013856887 and -3.013856887.Subproblem 1
x + 0.5 = 3.013856887 Simplifying x + 0.5 = 3.013856887 Reorder the terms: 0.5 + x = 3.013856887 Solving 0.5 + x = 3.013856887 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 = 3.013856887 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.013856887 + -0.5 x = 3.013856887 + -0.5 Combine like terms: 3.013856887 + -0.5 = 2.513856887 x = 2.513856887 Simplifying x = 2.513856887Subproblem 2
x + 0.5 = -3.013856887 Simplifying x + 0.5 = -3.013856887 Reorder the terms: 0.5 + x = -3.013856887 Solving 0.5 + x = -3.013856887 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 = -3.013856887 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.013856887 + -0.5 x = -3.013856887 + -0.5 Combine like terms: -3.013856887 + -0.5 = -3.513856887 x = -3.513856887 Simplifying x = -3.513856887Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.513856887, -3.513856887}
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