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Simplifying 2.94x2 + -24.99x + -13.23 = 0 Reorder the terms: -13.23 + -24.99x + 2.94x2 = 0 Solving -13.23 + -24.99x + 2.94x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.94 the coefficient of the squared term: Divide each side by '2.94'. -4.5 + -8.5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -8.5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -8.5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -8.5x + x2 = 0 + 4.5 -8.5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -8.5x + x2 = 4.5 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = 4.5 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = 4.5 + 18.0625 Combine like terms: 4.5 + 18.0625 = 22.5625 18.0625 + -8.5x + x2 = 22.5625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 22.5625 Calculate the square root of the right side: 4.75 Break this problem into two subproblems by setting (x + -4.25) equal to 4.75 and -4.75.Subproblem 1
x + -4.25 = 4.75 Simplifying x + -4.25 = 4.75 Reorder the terms: -4.25 + x = 4.75 Solving -4.25 + x = 4.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 4.75 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 4.75 + 4.25 x = 4.75 + 4.25 Combine like terms: 4.75 + 4.25 = 9 x = 9 Simplifying x = 9Subproblem 2
x + -4.25 = -4.75 Simplifying x + -4.25 = -4.75 Reorder the terms: -4.25 + x = -4.75 Solving -4.25 + x = -4.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -4.75 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -4.75 + 4.25 x = -4.75 + 4.25 Combine like terms: -4.75 + 4.25 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {9, -0.5}
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