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Simplifying 9x2 + 4x = 12 Reorder the terms: 4x + 9x2 = 12 Solving 4x + 9x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 4x + 9x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.333333333 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 0.4444444444x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 0.4444444444x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 0.4444444444x + x2 = 0 + 1.333333333 0.4444444444x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 0.4444444444x + x2 = 1.333333333 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 1.333333333 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 1.333333333 + 0.04938271604 Combine like terms: 1.333333333 + 0.04938271604 = 1.38271604904 0.04938271604 + 0.4444444444x + x2 = 1.38271604904 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 1.38271604904 Calculate the square root of the right side: 1.175889471 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 1.175889471 and -1.175889471.Subproblem 1
x + 0.2222222222 = 1.175889471 Simplifying x + 0.2222222222 = 1.175889471 Reorder the terms: 0.2222222222 + x = 1.175889471 Solving 0.2222222222 + x = 1.175889471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 1.175889471 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 1.175889471 + -0.2222222222 x = 1.175889471 + -0.2222222222 Combine like terms: 1.175889471 + -0.2222222222 = 0.9536672488 x = 0.9536672488 Simplifying x = 0.9536672488Subproblem 2
x + 0.2222222222 = -1.175889471 Simplifying x + 0.2222222222 = -1.175889471 Reorder the terms: 0.2222222222 + x = -1.175889471 Solving 0.2222222222 + x = -1.175889471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -1.175889471 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -1.175889471 + -0.2222222222 x = -1.175889471 + -0.2222222222 Combine like terms: -1.175889471 + -0.2222222222 = -1.3981116932 x = -1.3981116932 Simplifying x = -1.3981116932Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9536672488, -1.3981116932}
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