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Simplifying 4x + -9x2 = -324 Solving 4x + -9x2 = -324 Solving for variable 'x'. Reorder the terms: 324 + 4x + -9x2 = -324 + 324 Combine like terms: -324 + 324 = 0 324 + 4x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -36 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -0.4444444444x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -0.4444444444x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -0.4444444444x + x2 = 0 + 36 -0.4444444444x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -0.4444444444x + x2 = 36 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 = 36 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = 36 + 0.04938271604 Combine like terms: 36 + 0.04938271604 = 36.04938271604 0.04938271604 + -0.4444444444x + x2 = 36.04938271604 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = 36.04938271604 Calculate the square root of the right side: 6.004113816 Break this problem into two subproblems by setting (x + -0.2222222222) equal to 6.004113816 and -6.004113816.Subproblem 1
x + -0.2222222222 = 6.004113816 Simplifying x + -0.2222222222 = 6.004113816 Reorder the terms: -0.2222222222 + x = 6.004113816 Solving -0.2222222222 + x = 6.004113816 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 = 6.004113816 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 6.004113816 + 0.2222222222 x = 6.004113816 + 0.2222222222 Combine like terms: 6.004113816 + 0.2222222222 = 6.2263360382 x = 6.2263360382 Simplifying x = 6.2263360382Subproblem 2
x + -0.2222222222 = -6.004113816 Simplifying x + -0.2222222222 = -6.004113816 Reorder the terms: -0.2222222222 + x = -6.004113816 Solving -0.2222222222 + x = -6.004113816 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 = -6.004113816 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -6.004113816 + 0.2222222222 x = -6.004113816 + 0.2222222222 Combine like terms: -6.004113816 + 0.2222222222 = -5.7818915938 x = -5.7818915938 Simplifying x = -5.7818915938Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.2263360382, -5.7818915938}
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