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Simplifying -2x2 + 7x + 69 = 0 Reorder the terms: 69 + 7x + -2x2 = 0 Solving 69 + 7x + -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'. -34.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '34.5' to each side of the equation. -34.5 + -3.5x + 34.5 + x2 = 0 + 34.5 Reorder the terms: -34.5 + 34.5 + -3.5x + x2 = 0 + 34.5 Combine like terms: -34.5 + 34.5 = 0.0 0.0 + -3.5x + x2 = 0 + 34.5 -3.5x + x2 = 0 + 34.5 Combine like terms: 0 + 34.5 = 34.5 -3.5x + x2 = 34.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 34.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 34.5 + 3.0625 Combine like terms: 34.5 + 3.0625 = 37.5625 3.0625 + -3.5x + x2 = 37.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 37.5625 Calculate the square root of the right side: 6.128825336 Break this problem into two subproblems by setting (x + -1.75) equal to 6.128825336 and -6.128825336.Subproblem 1
x + -1.75 = 6.128825336 Simplifying x + -1.75 = 6.128825336 Reorder the terms: -1.75 + x = 6.128825336 Solving -1.75 + x = 6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 6.128825336 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 6.128825336 + 1.75 x = 6.128825336 + 1.75 Combine like terms: 6.128825336 + 1.75 = 7.878825336 x = 7.878825336 Simplifying x = 7.878825336Subproblem 2
x + -1.75 = -6.128825336 Simplifying x + -1.75 = -6.128825336 Reorder the terms: -1.75 + x = -6.128825336 Solving -1.75 + x = -6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -6.128825336 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -6.128825336 + 1.75 x = -6.128825336 + 1.75 Combine like terms: -6.128825336 + 1.75 = -4.378825336 x = -4.378825336 Simplifying x = -4.378825336Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.878825336, -4.378825336}
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