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Simplifying -8x2 + 18x + 25 = 0 Reorder the terms: 25 + 18x + -8x2 = 0 Solving 25 + 18x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + -2.25x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -2.25x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -2.25x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -2.25x + x2 = 0 + 3.125 -2.25x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -2.25x + x2 = 3.125 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 3.125 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 3.125 + 1.265625 Combine like terms: 3.125 + 1.265625 = 4.390625 1.265625 + -2.25x + x2 = 4.390625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (x + -1.125) equal to 2.095381827 and -2.095381827.Subproblem 1
x + -1.125 = 2.095381827 Simplifying x + -1.125 = 2.095381827 Reorder the terms: -1.125 + x = 2.095381827 Solving -1.125 + x = 2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 2.095381827 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 2.095381827 + 1.125 x = 2.095381827 + 1.125 Combine like terms: 2.095381827 + 1.125 = 3.220381827 x = 3.220381827 Simplifying x = 3.220381827Subproblem 2
x + -1.125 = -2.095381827 Simplifying x + -1.125 = -2.095381827 Reorder the terms: -1.125 + x = -2.095381827 Solving -1.125 + x = -2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -2.095381827 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -2.095381827 + 1.125 x = -2.095381827 + 1.125 Combine like terms: -2.095381827 + 1.125 = -0.970381827 x = -0.970381827 Simplifying x = -0.970381827Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.220381827, -0.970381827}
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