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Simplifying 2x2 + 9x = 72 Reorder the terms: 9x + 2x2 = 72 Solving 9x + 2x2 = 72 Solving for variable 'x'. Reorder the terms: -72 + 9x + 2x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -72 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -36 + 4.5x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 4.5x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 4.5x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 4.5x + x2 = 0 + 36 4.5x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 4.5x + x2 = 36 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 = 36 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 36 + 5.0625 Combine like terms: 36 + 5.0625 = 41.0625 5.0625 + 4.5x + x2 = 41.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 41.0625 Calculate the square root of the right side: 6.408002809 Break this problem into two subproblems by setting (x + 2.25) equal to 6.408002809 and -6.408002809.Subproblem 1
x + 2.25 = 6.408002809 Simplifying x + 2.25 = 6.408002809 Reorder the terms: 2.25 + x = 6.408002809 Solving 2.25 + x = 6.408002809 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 = 6.408002809 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 6.408002809 + -2.25 x = 6.408002809 + -2.25 Combine like terms: 6.408002809 + -2.25 = 4.158002809 x = 4.158002809 Simplifying x = 4.158002809Subproblem 2
x + 2.25 = -6.408002809 Simplifying x + 2.25 = -6.408002809 Reorder the terms: 2.25 + x = -6.408002809 Solving 2.25 + x = -6.408002809 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 = -6.408002809 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -6.408002809 + -2.25 x = -6.408002809 + -2.25 Combine like terms: -6.408002809 + -2.25 = -8.658002809 x = -8.658002809 Simplifying x = -8.658002809Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.158002809, -8.658002809}
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