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Simplifying 9x + 9 = 16x2 Reorder the terms: 9 + 9x = 16x2 Solving 9 + 9x = 16x2 Solving for variable 'x'. Combine like terms: 16x2 + -16x2 = 0 9 + 9x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.5625 + -0.5625x + x2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -0.5625x + 0.5625 + x2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -0.5625x + x2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -0.5625x + x2 = 0 + 0.5625 -0.5625x + x2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 -0.5625x + x2 = 0.5625 The x term is -0.5625x. Take half its coefficient (-0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. -0.5625x + 0.0791015625 + x2 = 0.5625 + 0.0791015625 Reorder the terms: 0.0791015625 + -0.5625x + x2 = 0.5625 + 0.0791015625 Combine like terms: 0.5625 + 0.0791015625 = 0.6416015625 0.0791015625 + -0.5625x + x2 = 0.6416015625 Factor a perfect square on the left side: (x + -0.28125)(x + -0.28125) = 0.6416015625 Calculate the square root of the right side: 0.801000351 Break this problem into two subproblems by setting (x + -0.28125) equal to 0.801000351 and -0.801000351.Subproblem 1
x + -0.28125 = 0.801000351 Simplifying x + -0.28125 = 0.801000351 Reorder the terms: -0.28125 + x = 0.801000351 Solving -0.28125 + x = 0.801000351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = 0.801000351 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = 0.801000351 + 0.28125 x = 0.801000351 + 0.28125 Combine like terms: 0.801000351 + 0.28125 = 1.082250351 x = 1.082250351 Simplifying x = 1.082250351Subproblem 2
x + -0.28125 = -0.801000351 Simplifying x + -0.28125 = -0.801000351 Reorder the terms: -0.28125 + x = -0.801000351 Solving -0.28125 + x = -0.801000351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = -0.801000351 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = -0.801000351 + 0.28125 x = -0.801000351 + 0.28125 Combine like terms: -0.801000351 + 0.28125 = -0.519750351 x = -0.519750351 Simplifying x = -0.519750351Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.082250351, -0.519750351}
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