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Simplifying 9x(27x + 11) = 14x + 6(17x + 5) Reorder the terms: 9x(11 + 27x) = 14x + 6(17x + 5) (11 * 9x + 27x * 9x) = 14x + 6(17x + 5) (99x + 243x2) = 14x + 6(17x + 5) Reorder the terms: 99x + 243x2 = 14x + 6(5 + 17x) 99x + 243x2 = 14x + (5 * 6 + 17x * 6) 99x + 243x2 = 14x + (30 + 102x) Reorder the terms: 99x + 243x2 = 30 + 14x + 102x Combine like terms: 14x + 102x = 116x 99x + 243x2 = 30 + 116x Solving 99x + 243x2 = 30 + 116x Solving for variable 'x'. Reorder the terms: -30 + 99x + -116x + 243x2 = 30 + 116x + -30 + -116x Combine like terms: 99x + -116x = -17x -30 + -17x + 243x2 = 30 + 116x + -30 + -116x Reorder the terms: -30 + -17x + 243x2 = 30 + -30 + 116x + -116x Combine like terms: 30 + -30 = 0 -30 + -17x + 243x2 = 0 + 116x + -116x -30 + -17x + 243x2 = 116x + -116x Combine like terms: 116x + -116x = 0 -30 + -17x + 243x2 = 0 Begin completing the square. Divide all terms by 243 the coefficient of the squared term: Divide each side by '243'. -0.1234567901 + -0.06995884774x + x2 = 0 Move the constant term to the right: Add '0.1234567901' to each side of the equation. -0.1234567901 + -0.06995884774x + 0.1234567901 + x2 = 0 + 0.1234567901 Reorder the terms: -0.1234567901 + 0.1234567901 + -0.06995884774x + x2 = 0 + 0.1234567901 Combine like terms: -0.1234567901 + 0.1234567901 = 0.0000000000 0.0000000000 + -0.06995884774x + x2 = 0 + 0.1234567901 -0.06995884774x + x2 = 0 + 0.1234567901 Combine like terms: 0 + 0.1234567901 = 0.1234567901 -0.06995884774x + x2 = 0.1234567901 The x term is -0.06995884774x. Take half its coefficient (-0.03497942387). Square it (0.001223560094) and add it to both sides. Add '0.001223560094' to each side of the equation. -0.06995884774x + 0.001223560094 + x2 = 0.1234567901 + 0.001223560094 Reorder the terms: 0.001223560094 + -0.06995884774x + x2 = 0.1234567901 + 0.001223560094 Combine like terms: 0.1234567901 + 0.001223560094 = 0.124680350194 0.001223560094 + -0.06995884774x + x2 = 0.124680350194 Factor a perfect square on the left side: (x + -0.03497942387)(x + -0.03497942387) = 0.124680350194 Calculate the square root of the right side: 0.353101048 Break this problem into two subproblems by setting (x + -0.03497942387) equal to 0.353101048 and -0.353101048.Subproblem 1
x + -0.03497942387 = 0.353101048 Simplifying x + -0.03497942387 = 0.353101048 Reorder the terms: -0.03497942387 + x = 0.353101048 Solving -0.03497942387 + x = 0.353101048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03497942387' to each side of the equation. -0.03497942387 + 0.03497942387 + x = 0.353101048 + 0.03497942387 Combine like terms: -0.03497942387 + 0.03497942387 = 0.00000000000 0.00000000000 + x = 0.353101048 + 0.03497942387 x = 0.353101048 + 0.03497942387 Combine like terms: 0.353101048 + 0.03497942387 = 0.38808047187 x = 0.38808047187 Simplifying x = 0.38808047187Subproblem 2
x + -0.03497942387 = -0.353101048 Simplifying x + -0.03497942387 = -0.353101048 Reorder the terms: -0.03497942387 + x = -0.353101048 Solving -0.03497942387 + x = -0.353101048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03497942387' to each side of the equation. -0.03497942387 + 0.03497942387 + x = -0.353101048 + 0.03497942387 Combine like terms: -0.03497942387 + 0.03497942387 = 0.00000000000 0.00000000000 + x = -0.353101048 + 0.03497942387 x = -0.353101048 + 0.03497942387 Combine like terms: -0.353101048 + 0.03497942387 = -0.31812162413 x = -0.31812162413 Simplifying x = -0.31812162413Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.38808047187, -0.31812162413}
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