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Simplifying 3x(x + 1) = 35 Reorder the terms: 3x(1 + x) = 35 (1 * 3x + x * 3x) = 35 (3x + 3x2) = 35 Solving 3x + 3x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + 3x + 3x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11.66666667 + x + x2 = 0 Move the constant term to the right: Add '11.66666667' to each side of the equation. -11.66666667 + x + 11.66666667 + x2 = 0 + 11.66666667 Reorder the terms: -11.66666667 + 11.66666667 + x + x2 = 0 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + x + x2 = 0 + 11.66666667 x + x2 = 0 + 11.66666667 Combine like terms: 0 + 11.66666667 = 11.66666667 x + x2 = 11.66666667 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 = 11.66666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 11.66666667 + 0.25 Combine like terms: 11.66666667 + 0.25 = 11.91666667 1.25 + x2 = 11.91666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 11.91666667 Calculate the square root of the right side: 3.45205253 Break this problem into two subproblems by setting (x + 0.5) equal to 3.45205253 and -3.45205253.Subproblem 1
x + 0.5 = 3.45205253 Simplifying x + 0.5 = 3.45205253 Reorder the terms: 0.5 + x = 3.45205253 Solving 0.5 + x = 3.45205253 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 = 3.45205253 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.45205253 + -0.5 x = 3.45205253 + -0.5 Combine like terms: 3.45205253 + -0.5 = 2.95205253 x = 2.95205253 Simplifying x = 2.95205253Subproblem 2
x + 0.5 = -3.45205253 Simplifying x + 0.5 = -3.45205253 Reorder the terms: 0.5 + x = -3.45205253 Solving 0.5 + x = -3.45205253 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 = -3.45205253 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.45205253 + -0.5 x = -3.45205253 + -0.5 Combine like terms: -3.45205253 + -0.5 = -3.95205253 x = -3.95205253 Simplifying x = -3.95205253Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.95205253, -3.95205253}
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