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Simplifying 2x2 + 9x + -42 = 0 Reorder the terms: -42 + 9x + 2x2 = 0 Solving -42 + 9x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21 + 4.5x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 4.5x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 4.5x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 4.5x + x2 = 0 + 21 4.5x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 4.5x + x2 = 21 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 = 21 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 21 + 5.0625 Combine like terms: 21 + 5.0625 = 26.0625 5.0625 + 4.5x + x2 = 26.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 26.0625 Calculate the square root of the right side: 5.105144464 Break this problem into two subproblems by setting (x + 2.25) equal to 5.105144464 and -5.105144464.Subproblem 1
x + 2.25 = 5.105144464 Simplifying x + 2.25 = 5.105144464 Reorder the terms: 2.25 + x = 5.105144464 Solving 2.25 + x = 5.105144464 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 = 5.105144464 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 5.105144464 + -2.25 x = 5.105144464 + -2.25 Combine like terms: 5.105144464 + -2.25 = 2.855144464 x = 2.855144464 Simplifying x = 2.855144464Subproblem 2
x + 2.25 = -5.105144464 Simplifying x + 2.25 = -5.105144464 Reorder the terms: 2.25 + x = -5.105144464 Solving 2.25 + x = -5.105144464 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 = -5.105144464 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -5.105144464 + -2.25 x = -5.105144464 + -2.25 Combine like terms: -5.105144464 + -2.25 = -7.355144464 x = -7.355144464 Simplifying x = -7.355144464Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.855144464, -7.355144464}
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