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Simplifying 0 = 5x2 + -45x + -28 Reorder the terms: 0 = -28 + -45x + 5x2 Solving 0 = -28 + -45x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 28 = 28 28 + 45x + -5x2 = -28 + -45x + 5x2 + 28 + 45x + -5x2 Reorder the terms: 28 + 45x + -5x2 = -28 + 28 + -45x + 45x + 5x2 + -5x2 Combine like terms: -28 + 28 = 0 28 + 45x + -5x2 = 0 + -45x + 45x + 5x2 + -5x2 28 + 45x + -5x2 = -45x + 45x + 5x2 + -5x2 Combine like terms: -45x + 45x = 0 28 + 45x + -5x2 = 0 + 5x2 + -5x2 28 + 45x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 28 + 45x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -5.6 + -9x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -9x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -9x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -9x + x2 = 0 + 5.6 -9x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -9x + x2 = 5.6 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 = 5.6 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 5.6 + 20.25 Combine like terms: 5.6 + 20.25 = 25.85 20.25 + -9x + x2 = 25.85 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 25.85 Calculate the square root of the right side: 5.084289528 Break this problem into two subproblems by setting (x + -4.5) equal to 5.084289528 and -5.084289528.Subproblem 1
x + -4.5 = 5.084289528 Simplifying x + -4.5 = 5.084289528 Reorder the terms: -4.5 + x = 5.084289528 Solving -4.5 + x = 5.084289528 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 = 5.084289528 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.084289528 + 4.5 x = 5.084289528 + 4.5 Combine like terms: 5.084289528 + 4.5 = 9.584289528 x = 9.584289528 Simplifying x = 9.584289528Subproblem 2
x + -4.5 = -5.084289528 Simplifying x + -4.5 = -5.084289528 Reorder the terms: -4.5 + x = -5.084289528 Solving -4.5 + x = -5.084289528 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 = -5.084289528 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.084289528 + 4.5 x = -5.084289528 + 4.5 Combine like terms: -5.084289528 + 4.5 = -0.584289528 x = -0.584289528 Simplifying x = -0.584289528Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.584289528, -0.584289528}
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