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Simplifying 0 = 2.65x2 + -17.23x + -9.28 Reorder the terms: 0 = -9.28 + -17.23x + 2.65x2 Solving 0 = -9.28 + -17.23x + 2.65x2 Solving for variable 'x'. Combine like terms: 0 + 9.28 = 9.28 9.28 + 17.23x + -2.65x2 = -9.28 + -17.23x + 2.65x2 + 9.28 + 17.23x + -2.65x2 Reorder the terms: 9.28 + 17.23x + -2.65x2 = -9.28 + 9.28 + -17.23x + 17.23x + 2.65x2 + -2.65x2 Combine like terms: -9.28 + 9.28 = 0.00 9.28 + 17.23x + -2.65x2 = 0.00 + -17.23x + 17.23x + 2.65x2 + -2.65x2 9.28 + 17.23x + -2.65x2 = -17.23x + 17.23x + 2.65x2 + -2.65x2 Combine like terms: -17.23x + 17.23x = 0.00 9.28 + 17.23x + -2.65x2 = 0.00 + 2.65x2 + -2.65x2 9.28 + 17.23x + -2.65x2 = 2.65x2 + -2.65x2 Combine like terms: 2.65x2 + -2.65x2 = 0.00 9.28 + 17.23x + -2.65x2 = 0.00 Begin completing the square. Divide all terms by -2.65 the coefficient of the squared term: Divide each side by '-2.65'. -3.501886792 + -6.501886792x + x2 = 0 Move the constant term to the right: Add '3.501886792' to each side of the equation. -3.501886792 + -6.501886792x + 3.501886792 + x2 = 0 + 3.501886792 Reorder the terms: -3.501886792 + 3.501886792 + -6.501886792x + x2 = 0 + 3.501886792 Combine like terms: -3.501886792 + 3.501886792 = 0.000000000 0.000000000 + -6.501886792x + x2 = 0 + 3.501886792 -6.501886792x + x2 = 0 + 3.501886792 Combine like terms: 0 + 3.501886792 = 3.501886792 -6.501886792x + x2 = 3.501886792 The x term is -6.501886792x. Take half its coefficient (-3.250943396). Square it (10.56863296) and add it to both sides. Add '10.56863296' to each side of the equation. -6.501886792x + 10.56863296 + x2 = 3.501886792 + 10.56863296 Reorder the terms: 10.56863296 + -6.501886792x + x2 = 3.501886792 + 10.56863296 Combine like terms: 3.501886792 + 10.56863296 = 14.070519752 10.56863296 + -6.501886792x + x2 = 14.070519752 Factor a perfect square on the left side: (x + -3.250943396)(x + -3.250943396) = 14.070519752 Calculate the square root of the right side: 3.751069148 Break this problem into two subproblems by setting (x + -3.250943396) equal to 3.751069148 and -3.751069148.Subproblem 1
x + -3.250943396 = 3.751069148 Simplifying x + -3.250943396 = 3.751069148 Reorder the terms: -3.250943396 + x = 3.751069148 Solving -3.250943396 + x = 3.751069148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.250943396' to each side of the equation. -3.250943396 + 3.250943396 + x = 3.751069148 + 3.250943396 Combine like terms: -3.250943396 + 3.250943396 = 0.000000000 0.000000000 + x = 3.751069148 + 3.250943396 x = 3.751069148 + 3.250943396 Combine like terms: 3.751069148 + 3.250943396 = 7.002012544 x = 7.002012544 Simplifying x = 7.002012544Subproblem 2
x + -3.250943396 = -3.751069148 Simplifying x + -3.250943396 = -3.751069148 Reorder the terms: -3.250943396 + x = -3.751069148 Solving -3.250943396 + x = -3.751069148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.250943396' to each side of the equation. -3.250943396 + 3.250943396 + x = -3.751069148 + 3.250943396 Combine like terms: -3.250943396 + 3.250943396 = 0.000000000 0.000000000 + x = -3.751069148 + 3.250943396 x = -3.751069148 + 3.250943396 Combine like terms: -3.751069148 + 3.250943396 = -0.500125752 x = -0.500125752 Simplifying x = -0.500125752Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.002012544, -0.500125752}
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