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Simplifying 2.7x + x2 = 45 Solving 2.7x + x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + 2.7x + x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + 2.7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 2.7x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 2.7x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 2.7x + x2 = 0 + 45 2.7x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 2.7x + x2 = 45 The x term is 2.7x. Take half its coefficient (1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. 2.7x + 1.8225 + x2 = 45 + 1.8225 Reorder the terms: 1.8225 + 2.7x + x2 = 45 + 1.8225 Combine like terms: 45 + 1.8225 = 46.8225 1.8225 + 2.7x + x2 = 46.8225 Factor a perfect square on the left side: (x + 1.35)(x + 1.35) = 46.8225 Calculate the square root of the right side: 6.842696837 Break this problem into two subproblems by setting (x + 1.35) equal to 6.842696837 and -6.842696837.Subproblem 1
x + 1.35 = 6.842696837 Simplifying x + 1.35 = 6.842696837 Reorder the terms: 1.35 + x = 6.842696837 Solving 1.35 + x = 6.842696837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + x = 6.842696837 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + x = 6.842696837 + -1.35 x = 6.842696837 + -1.35 Combine like terms: 6.842696837 + -1.35 = 5.492696837 x = 5.492696837 Simplifying x = 5.492696837Subproblem 2
x + 1.35 = -6.842696837 Simplifying x + 1.35 = -6.842696837 Reorder the terms: 1.35 + x = -6.842696837 Solving 1.35 + x = -6.842696837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.35' to each side of the equation. 1.35 + -1.35 + x = -6.842696837 + -1.35 Combine like terms: 1.35 + -1.35 = 0.00 0.00 + x = -6.842696837 + -1.35 x = -6.842696837 + -1.35 Combine like terms: -6.842696837 + -1.35 = -8.192696837 x = -8.192696837 Simplifying x = -8.192696837Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.492696837, -8.192696837}
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