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Simplifying 2x(x + 6) + -10 = 55 Reorder the terms: 2x(6 + x) + -10 = 55 (6 * 2x + x * 2x) + -10 = 55 (12x + 2x2) + -10 = 55 Reorder the terms: -10 + 12x + 2x2 = 55 Solving -10 + 12x + 2x2 = 55 Solving for variable 'x'. Reorder the terms: -10 + -55 + 12x + 2x2 = 55 + -55 Combine like terms: -10 + -55 = -65 -65 + 12x + 2x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -65 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -32.5 + 6x + x2 = 0 Move the constant term to the right: Add '32.5' to each side of the equation. -32.5 + 6x + 32.5 + x2 = 0 + 32.5 Reorder the terms: -32.5 + 32.5 + 6x + x2 = 0 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + 6x + x2 = 0 + 32.5 6x + x2 = 0 + 32.5 Combine like terms: 0 + 32.5 = 32.5 6x + x2 = 32.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 32.5 + 9 Reorder the terms: 9 + 6x + x2 = 32.5 + 9 Combine like terms: 32.5 + 9 = 41.5 9 + 6x + x2 = 41.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 41.5 Calculate the square root of the right side: 6.442049363 Break this problem into two subproblems by setting (x + 3) equal to 6.442049363 and -6.442049363.Subproblem 1
x + 3 = 6.442049363 Simplifying x + 3 = 6.442049363 Reorder the terms: 3 + x = 6.442049363 Solving 3 + x = 6.442049363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.442049363 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.442049363 + -3 x = 6.442049363 + -3 Combine like terms: 6.442049363 + -3 = 3.442049363 x = 3.442049363 Simplifying x = 3.442049363Subproblem 2
x + 3 = -6.442049363 Simplifying x + 3 = -6.442049363 Reorder the terms: 3 + x = -6.442049363 Solving 3 + x = -6.442049363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.442049363 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.442049363 + -3 x = -6.442049363 + -3 Combine like terms: -6.442049363 + -3 = -9.442049363 x = -9.442049363 Simplifying x = -9.442049363Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.442049363, -9.442049363}
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