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Simplifying 5x2 + -45x + 84 = 0 Reorder the terms: 84 + -45x + 5x2 = 0 Solving 84 + -45x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 16.8 + -9x + x2 = 0 Move the constant term to the right: Add '-16.8' to each side of the equation. 16.8 + -9x + -16.8 + x2 = 0 + -16.8 Reorder the terms: 16.8 + -16.8 + -9x + x2 = 0 + -16.8 Combine like terms: 16.8 + -16.8 = 0.0 0.0 + -9x + x2 = 0 + -16.8 -9x + x2 = 0 + -16.8 Combine like terms: 0 + -16.8 = -16.8 -9x + x2 = -16.8 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -16.8 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -16.8 + 20.25 Combine like terms: -16.8 + 20.25 = 3.45 20.25 + -9x + x2 = 3.45 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 3.45 Calculate the square root of the right side: 1.857417562 Break this problem into two subproblems by setting (x + -4.5) equal to 1.857417562 and -1.857417562.Subproblem 1
x + -4.5 = 1.857417562 Simplifying x + -4.5 = 1.857417562 Reorder the terms: -4.5 + x = 1.857417562 Solving -4.5 + x = 1.857417562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 1.857417562 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 1.857417562 + 4.5 x = 1.857417562 + 4.5 Combine like terms: 1.857417562 + 4.5 = 6.357417562 x = 6.357417562 Simplifying x = 6.357417562Subproblem 2
x + -4.5 = -1.857417562 Simplifying x + -4.5 = -1.857417562 Reorder the terms: -4.5 + x = -1.857417562 Solving -4.5 + x = -1.857417562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -1.857417562 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -1.857417562 + 4.5 x = -1.857417562 + 4.5 Combine like terms: -1.857417562 + 4.5 = 2.642582438 x = 2.642582438 Simplifying x = 2.642582438Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.357417562, 2.642582438}
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