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Simplifying 2.76x2 + -12.42x + -6.9 = 0 Reorder the terms: -6.9 + -12.42x + 2.76x2 = 0 Solving -6.9 + -12.42x + 2.76x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.76 the coefficient of the squared term: Divide each side by '2.76'. -2.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -4.5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -4.5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -4.5x + x2 = 0 + 2.5 -4.5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -4.5x + x2 = 2.5 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 = 2.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 2.5 + 5.0625 Combine like terms: 2.5 + 5.0625 = 7.5625 5.0625 + -4.5x + x2 = 7.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 7.5625 Calculate the square root of the right side: 2.75 Break this problem into two subproblems by setting (x + -2.25) equal to 2.75 and -2.75.Subproblem 1
x + -2.25 = 2.75 Simplifying x + -2.25 = 2.75 Reorder the terms: -2.25 + x = 2.75 Solving -2.25 + x = 2.75 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 = 2.75 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.75 + 2.25 x = 2.75 + 2.25 Combine like terms: 2.75 + 2.25 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -2.25 = -2.75 Simplifying x + -2.25 = -2.75 Reorder the terms: -2.25 + x = -2.75 Solving -2.25 + x = -2.75 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 = -2.75 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.75 + 2.25 x = -2.75 + 2.25 Combine like terms: -2.75 + 2.25 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, -0.5}
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