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Simplifying 9x(2x + -9) = 7 + 6 Reorder the terms: 9x(-9 + 2x) = 7 + 6 (-9 * 9x + 2x * 9x) = 7 + 6 (-81x + 18x2) = 7 + 6 Combine like terms: 7 + 6 = 13 -81x + 18x2 = 13 Solving -81x + 18x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -81x + 18x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -81x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.7222222222 + -4.5x + x2 = 0 Move the constant term to the right: Add '0.7222222222' to each side of the equation. -0.7222222222 + -4.5x + 0.7222222222 + x2 = 0 + 0.7222222222 Reorder the terms: -0.7222222222 + 0.7222222222 + -4.5x + x2 = 0 + 0.7222222222 Combine like terms: -0.7222222222 + 0.7222222222 = 0.0000000000 0.0000000000 + -4.5x + x2 = 0 + 0.7222222222 -4.5x + x2 = 0 + 0.7222222222 Combine like terms: 0 + 0.7222222222 = 0.7222222222 -4.5x + x2 = 0.7222222222 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 0.7222222222 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 0.7222222222 + 5.0625 Combine like terms: 0.7222222222 + 5.0625 = 5.7847222222 5.0625 + -4.5x + x2 = 5.7847222222 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 5.7847222222 Calculate the square root of the right side: 2.405144948 Break this problem into two subproblems by setting (x + -2.25) equal to 2.405144948 and -2.405144948.Subproblem 1
x + -2.25 = 2.405144948 Simplifying x + -2.25 = 2.405144948 Reorder the terms: -2.25 + x = 2.405144948 Solving -2.25 + x = 2.405144948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.405144948 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.405144948 + 2.25 x = 2.405144948 + 2.25 Combine like terms: 2.405144948 + 2.25 = 4.655144948 x = 4.655144948 Simplifying x = 4.655144948Subproblem 2
x + -2.25 = -2.405144948 Simplifying x + -2.25 = -2.405144948 Reorder the terms: -2.25 + x = -2.405144948 Solving -2.25 + x = -2.405144948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.405144948 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.405144948 + 2.25 x = -2.405144948 + 2.25 Combine like terms: -2.405144948 + 2.25 = -0.155144948 x = -0.155144948 Simplifying x = -0.155144948Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.655144948, -0.155144948}
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