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Simplifying 2x2 + 9x + -156 = 0 Reorder the terms: -156 + 9x + 2x2 = 0 Solving -156 + 9x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -78 + 4.5x + x2 = 0 Move the constant term to the right: Add '78' to each side of the equation. -78 + 4.5x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + 4.5x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + 4.5x + x2 = 0 + 78 4.5x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 4.5x + x2 = 78 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 = 78 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 78 + 5.0625 Combine like terms: 78 + 5.0625 = 83.0625 5.0625 + 4.5x + x2 = 83.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 83.0625 Calculate the square root of the right side: 9.113863067 Break this problem into two subproblems by setting (x + 2.25) equal to 9.113863067 and -9.113863067.Subproblem 1
x + 2.25 = 9.113863067 Simplifying x + 2.25 = 9.113863067 Reorder the terms: 2.25 + x = 9.113863067 Solving 2.25 + x = 9.113863067 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 = 9.113863067 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 9.113863067 + -2.25 x = 9.113863067 + -2.25 Combine like terms: 9.113863067 + -2.25 = 6.863863067 x = 6.863863067 Simplifying x = 6.863863067Subproblem 2
x + 2.25 = -9.113863067 Simplifying x + 2.25 = -9.113863067 Reorder the terms: 2.25 + x = -9.113863067 Solving 2.25 + x = -9.113863067 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 = -9.113863067 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -9.113863067 + -2.25 x = -9.113863067 + -2.25 Combine like terms: -9.113863067 + -2.25 = -11.363863067 x = -11.363863067 Simplifying x = -11.363863067Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.863863067, -11.363863067}
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