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Simplifying 2x(x + 3) = 2x + 2x + 15 Reorder the terms: 2x(3 + x) = 2x + 2x + 15 (3 * 2x + x * 2x) = 2x + 2x + 15 (6x + 2x2) = 2x + 2x + 15 Reorder the terms: 6x + 2x2 = 15 + 2x + 2x Combine like terms: 2x + 2x = 4x 6x + 2x2 = 15 + 4x Solving 6x + 2x2 = 15 + 4x Solving for variable 'x'. Reorder the terms: -15 + 6x + -4x + 2x2 = 15 + 4x + -15 + -4x Combine like terms: 6x + -4x = 2x -15 + 2x + 2x2 = 15 + 4x + -15 + -4x Reorder the terms: -15 + 2x + 2x2 = 15 + -15 + 4x + -4x Combine like terms: 15 + -15 = 0 -15 + 2x + 2x2 = 0 + 4x + -4x -15 + 2x + 2x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -15 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x + x2 = 0 + 7.5 x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 x + x2 = 7.5 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 = 7.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 7.5 + 0.25 Combine like terms: 7.5 + 0.25 = 7.75 1.25 + x2 = 7.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (x + 0.5) equal to 2.783882181 and -2.783882181.Subproblem 1
x + 0.5 = 2.783882181 Simplifying x + 0.5 = 2.783882181 Reorder the terms: 0.5 + x = 2.783882181 Solving 0.5 + x = 2.783882181 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 = 2.783882181 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.783882181 + -0.5 x = 2.783882181 + -0.5 Combine like terms: 2.783882181 + -0.5 = 2.283882181 x = 2.283882181 Simplifying x = 2.283882181Subproblem 2
x + 0.5 = -2.783882181 Simplifying x + 0.5 = -2.783882181 Reorder the terms: 0.5 + x = -2.783882181 Solving 0.5 + x = -2.783882181 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 = -2.783882181 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.783882181 + -0.5 x = -2.783882181 + -0.5 Combine like terms: -2.783882181 + -0.5 = -3.283882181 x = -3.283882181 Simplifying x = -3.283882181Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.283882181, -3.283882181}
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