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Simplifying 3x2 + 3x = 110 Reorder the terms: 3x + 3x2 = 110 Solving 3x + 3x2 = 110 Solving for variable 'x'. Reorder the terms: -110 + 3x + 3x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -36.66666667 + x + x2 = 0 Move the constant term to the right: Add '36.66666667' to each side of the equation. -36.66666667 + x + 36.66666667 + x2 = 0 + 36.66666667 Reorder the terms: -36.66666667 + 36.66666667 + x + x2 = 0 + 36.66666667 Combine like terms: -36.66666667 + 36.66666667 = 0.00000000 0.00000000 + x + x2 = 0 + 36.66666667 x + x2 = 0 + 36.66666667 Combine like terms: 0 + 36.66666667 = 36.66666667 x + x2 = 36.66666667 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 = 36.66666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 36.66666667 + 0.25 Combine like terms: 36.66666667 + 0.25 = 36.91666667 1.25 + x2 = 36.91666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 36.91666667 Calculate the square root of the right side: 6.075908711 Break this problem into two subproblems by setting (x + 0.5) equal to 6.075908711 and -6.075908711.Subproblem 1
x + 0.5 = 6.075908711 Simplifying x + 0.5 = 6.075908711 Reorder the terms: 0.5 + x = 6.075908711 Solving 0.5 + x = 6.075908711 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 = 6.075908711 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.075908711 + -0.5 x = 6.075908711 + -0.5 Combine like terms: 6.075908711 + -0.5 = 5.575908711 x = 5.575908711 Simplifying x = 5.575908711Subproblem 2
x + 0.5 = -6.075908711 Simplifying x + 0.5 = -6.075908711 Reorder the terms: 0.5 + x = -6.075908711 Solving 0.5 + x = -6.075908711 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 = -6.075908711 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.075908711 + -0.5 x = -6.075908711 + -0.5 Combine like terms: -6.075908711 + -0.5 = -6.575908711 x = -6.575908711 Simplifying x = -6.575908711Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.575908711, -6.575908711}
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