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Simplifying 4x2 + -17x + -69 = 0 Reorder the terms: -69 + -17x + 4x2 = 0 Solving -69 + -17x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -17.25 + -4.25x + x2 = 0 Move the constant term to the right: Add '17.25' to each side of the equation. -17.25 + -4.25x + 17.25 + x2 = 0 + 17.25 Reorder the terms: -17.25 + 17.25 + -4.25x + x2 = 0 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + -4.25x + x2 = 0 + 17.25 -4.25x + x2 = 0 + 17.25 Combine like terms: 0 + 17.25 = 17.25 -4.25x + x2 = 17.25 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = 17.25 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = 17.25 + 4.515625 Combine like terms: 17.25 + 4.515625 = 21.765625 4.515625 + -4.25x + x2 = 21.765625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 21.765625 Calculate the square root of the right side: 4.665364402 Break this problem into two subproblems by setting (x + -2.125) equal to 4.665364402 and -4.665364402.Subproblem 1
x + -2.125 = 4.665364402 Simplifying x + -2.125 = 4.665364402 Reorder the terms: -2.125 + x = 4.665364402 Solving -2.125 + x = 4.665364402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 4.665364402 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 4.665364402 + 2.125 x = 4.665364402 + 2.125 Combine like terms: 4.665364402 + 2.125 = 6.790364402 x = 6.790364402 Simplifying x = 6.790364402Subproblem 2
x + -2.125 = -4.665364402 Simplifying x + -2.125 = -4.665364402 Reorder the terms: -2.125 + x = -4.665364402 Solving -2.125 + x = -4.665364402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -4.665364402 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -4.665364402 + 2.125 x = -4.665364402 + 2.125 Combine like terms: -4.665364402 + 2.125 = -2.540364402 x = -2.540364402 Simplifying x = -2.540364402Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.790364402, -2.540364402}
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