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Simplifying 7x(2x + -9) = 180 Reorder the terms: 7x(-9 + 2x) = 180 (-9 * 7x + 2x * 7x) = 180 (-63x + 14x2) = 180 Solving -63x + 14x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -63x + 14x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -63x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -12.85714286 + -4.5x + x2 = 0 Move the constant term to the right: Add '12.85714286' to each side of the equation. -12.85714286 + -4.5x + 12.85714286 + x2 = 0 + 12.85714286 Reorder the terms: -12.85714286 + 12.85714286 + -4.5x + x2 = 0 + 12.85714286 Combine like terms: -12.85714286 + 12.85714286 = 0.00000000 0.00000000 + -4.5x + x2 = 0 + 12.85714286 -4.5x + x2 = 0 + 12.85714286 Combine like terms: 0 + 12.85714286 = 12.85714286 -4.5x + x2 = 12.85714286 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 = 12.85714286 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 12.85714286 + 5.0625 Combine like terms: 12.85714286 + 5.0625 = 17.91964286 5.0625 + -4.5x + x2 = 17.91964286 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 17.91964286 Calculate the square root of the right side: 4.233159914 Break this problem into two subproblems by setting (x + -2.25) equal to 4.233159914 and -4.233159914.Subproblem 1
x + -2.25 = 4.233159914 Simplifying x + -2.25 = 4.233159914 Reorder the terms: -2.25 + x = 4.233159914 Solving -2.25 + x = 4.233159914 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 = 4.233159914 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 4.233159914 + 2.25 x = 4.233159914 + 2.25 Combine like terms: 4.233159914 + 2.25 = 6.483159914 x = 6.483159914 Simplifying x = 6.483159914Subproblem 2
x + -2.25 = -4.233159914 Simplifying x + -2.25 = -4.233159914 Reorder the terms: -2.25 + x = -4.233159914 Solving -2.25 + x = -4.233159914 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 = -4.233159914 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -4.233159914 + 2.25 x = -4.233159914 + 2.25 Combine like terms: -4.233159914 + 2.25 = -1.983159914 x = -1.983159914 Simplifying x = -1.983159914Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.483159914, -1.983159914}
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