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Simplifying 2x(x + 3) + 3x = 13 Reorder the terms: 2x(3 + x) + 3x = 13 (3 * 2x + x * 2x) + 3x = 13 (6x + 2x2) + 3x = 13 Reorder the terms: 6x + 3x + 2x2 = 13 Combine like terms: 6x + 3x = 9x 9x + 2x2 = 13 Solving 9x + 2x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 9x + 2x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 4.5x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 4.5x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 4.5x + x2 = 0 + 6.5 4.5x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 4.5x + x2 = 6.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 6.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 6.5 + 5.0625 Combine like terms: 6.5 + 5.0625 = 11.5625 5.0625 + 4.5x + x2 = 11.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (x + 2.25) equal to 3.400367627 and -3.400367627.Subproblem 1
x + 2.25 = 3.400367627 Simplifying x + 2.25 = 3.400367627 Reorder the terms: 2.25 + x = 3.400367627 Solving 2.25 + x = 3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 3.400367627 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 3.400367627 + -2.25 x = 3.400367627 + -2.25 Combine like terms: 3.400367627 + -2.25 = 1.150367627 x = 1.150367627 Simplifying x = 1.150367627Subproblem 2
x + 2.25 = -3.400367627 Simplifying x + 2.25 = -3.400367627 Reorder the terms: 2.25 + x = -3.400367627 Solving 2.25 + x = -3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -3.400367627 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -3.400367627 + -2.25 x = -3.400367627 + -2.25 Combine like terms: -3.400367627 + -2.25 = -5.650367627 x = -5.650367627 Simplifying x = -5.650367627Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.150367627, -5.650367627}
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