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Simplifying 0.3x2 + -2.7x + 4.2 = 0 Reorder the terms: 4.2 + -2.7x + 0.3x2 = 0 Solving 4.2 + -2.7x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 14 + -9x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -9x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -9x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -9x + x2 = 0 + -14 -9x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -9x + x2 = -14 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 = -14 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -14 + 20.25 Combine like terms: -14 + 20.25 = 6.25 20.25 + -9x + x2 = 6.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + -4.5) equal to 2.5 and -2.5.Subproblem 1
x + -4.5 = 2.5 Simplifying x + -4.5 = 2.5 Reorder the terms: -4.5 + x = 2.5 Solving -4.5 + x = 2.5 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 = 2.5 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 2.5 + 4.5 x = 2.5 + 4.5 Combine like terms: 2.5 + 4.5 = 7 x = 7 Simplifying x = 7Subproblem 2
x + -4.5 = -2.5 Simplifying x + -4.5 = -2.5 Reorder the terms: -4.5 + x = -2.5 Solving -4.5 + x = -2.5 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 = -2.5 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -2.5 + 4.5 x = -2.5 + 4.5 Combine like terms: -2.5 + 4.5 = 2 x = 2 Simplifying x = 2Solution
The solution to the problem is based on the solutions from the subproblems. x = {7, 2}
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