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Simplifying 0 = 4x2 + 18x + -9 Reorder the terms: 0 = -9 + 18x + 4x2 Solving 0 = -9 + 18x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 9 = 9 9 + -18x + -4x2 = -9 + 18x + 4x2 + 9 + -18x + -4x2 Reorder the terms: 9 + -18x + -4x2 = -9 + 9 + 18x + -18x + 4x2 + -4x2 Combine like terms: -9 + 9 = 0 9 + -18x + -4x2 = 0 + 18x + -18x + 4x2 + -4x2 9 + -18x + -4x2 = 18x + -18x + 4x2 + -4x2 Combine like terms: 18x + -18x = 0 9 + -18x + -4x2 = 0 + 4x2 + -4x2 9 + -18x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 9 + -18x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.25 + 4.5x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 4.5x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 4.5x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 4.5x + x2 = 0 + 2.25 4.5x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 4.5x + x2 = 2.25 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 = 2.25 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 2.25 + 5.0625 Combine like terms: 2.25 + 5.0625 = 7.3125 5.0625 + 4.5x + x2 = 7.3125 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 7.3125 Calculate the square root of the right side: 2.704163457 Break this problem into two subproblems by setting (x + 2.25) equal to 2.704163457 and -2.704163457.Subproblem 1
x + 2.25 = 2.704163457 Simplifying x + 2.25 = 2.704163457 Reorder the terms: 2.25 + x = 2.704163457 Solving 2.25 + x = 2.704163457 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 = 2.704163457 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.704163457 + -2.25 x = 2.704163457 + -2.25 Combine like terms: 2.704163457 + -2.25 = 0.454163457 x = 0.454163457 Simplifying x = 0.454163457Subproblem 2
x + 2.25 = -2.704163457 Simplifying x + 2.25 = -2.704163457 Reorder the terms: 2.25 + x = -2.704163457 Solving 2.25 + x = -2.704163457 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 = -2.704163457 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.704163457 + -2.25 x = -2.704163457 + -2.25 Combine like terms: -2.704163457 + -2.25 = -4.954163457 x = -4.954163457 Simplifying x = -4.954163457Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.454163457, -4.954163457}
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