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Simplifying 2x(x + 6) = 9 + -14x Reorder the terms: 2x(6 + x) = 9 + -14x (6 * 2x + x * 2x) = 9 + -14x (12x + 2x2) = 9 + -14x Solving 12x + 2x2 = 9 + -14x Solving for variable 'x'. Reorder the terms: -9 + 12x + 14x + 2x2 = 9 + -14x + -9 + 14x Combine like terms: 12x + 14x = 26x -9 + 26x + 2x2 = 9 + -14x + -9 + 14x Reorder the terms: -9 + 26x + 2x2 = 9 + -9 + -14x + 14x Combine like terms: 9 + -9 = 0 -9 + 26x + 2x2 = 0 + -14x + 14x -9 + 26x + 2x2 = -14x + 14x Combine like terms: -14x + 14x = 0 -9 + 26x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 13x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 13x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 13x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 13x + x2 = 0 + 4.5 13x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 13x + x2 = 4.5 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 4.5 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 4.5 + 42.25 Combine like terms: 4.5 + 42.25 = 46.75 42.25 + 13x + x2 = 46.75 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 46.75 Calculate the square root of the right side: 6.837397166 Break this problem into two subproblems by setting (x + 6.5) equal to 6.837397166 and -6.837397166.Subproblem 1
x + 6.5 = 6.837397166 Simplifying x + 6.5 = 6.837397166 Reorder the terms: 6.5 + x = 6.837397166 Solving 6.5 + x = 6.837397166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 6.837397166 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 6.837397166 + -6.5 x = 6.837397166 + -6.5 Combine like terms: 6.837397166 + -6.5 = 0.337397166 x = 0.337397166 Simplifying x = 0.337397166Subproblem 2
x + 6.5 = -6.837397166 Simplifying x + 6.5 = -6.837397166 Reorder the terms: 6.5 + x = -6.837397166 Solving 6.5 + x = -6.837397166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -6.837397166 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -6.837397166 + -6.5 x = -6.837397166 + -6.5 Combine like terms: -6.837397166 + -6.5 = -13.337397166 x = -13.337397166 Simplifying x = -13.337397166Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.337397166, -13.337397166}
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