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Simplifying -16x2 + -45x + -18 = 0 Reorder the terms: -18 + -45x + -16x2 = 0 Solving -18 + -45x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(18 + 45x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(18 + 45x + 16x2)' equal to zero and attempt to solve: Simplifying 18 + 45x + 16x2 = 0 Solving 18 + 45x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.125 + 2.8125x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + 2.8125x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + 2.8125x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + 2.8125x + x2 = 0 + -1.125 2.8125x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 2.8125x + x2 = -1.125 The x term is 2.8125x. Take half its coefficient (1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. 2.8125x + 1.977539063 + x2 = -1.125 + 1.977539063 Reorder the terms: 1.977539063 + 2.8125x + x2 = -1.125 + 1.977539063 Combine like terms: -1.125 + 1.977539063 = 0.852539063 1.977539063 + 2.8125x + x2 = 0.852539063 Factor a perfect square on the left side: (x + 1.40625)(x + 1.40625) = 0.852539063 Calculate the square root of the right side: 0.923330419 Break this problem into two subproblems by setting (x + 1.40625) equal to 0.923330419 and -0.923330419.Subproblem 1
x + 1.40625 = 0.923330419 Simplifying x + 1.40625 = 0.923330419 Reorder the terms: 1.40625 + x = 0.923330419 Solving 1.40625 + x = 0.923330419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.40625' to each side of the equation. 1.40625 + -1.40625 + x = 0.923330419 + -1.40625 Combine like terms: 1.40625 + -1.40625 = 0.00000 0.00000 + x = 0.923330419 + -1.40625 x = 0.923330419 + -1.40625 Combine like terms: 0.923330419 + -1.40625 = -0.482919581 x = -0.482919581 Simplifying x = -0.482919581Subproblem 2
x + 1.40625 = -0.923330419 Simplifying x + 1.40625 = -0.923330419 Reorder the terms: 1.40625 + x = -0.923330419 Solving 1.40625 + x = -0.923330419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.40625' to each side of the equation. 1.40625 + -1.40625 + x = -0.923330419 + -1.40625 Combine like terms: 1.40625 + -1.40625 = 0.00000 0.00000 + x = -0.923330419 + -1.40625 x = -0.923330419 + -1.40625 Combine like terms: -0.923330419 + -1.40625 = -2.329580419 x = -2.329580419 Simplifying x = -2.329580419Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.482919581, -2.329580419}Solution
x = {-0.482919581, -2.329580419}
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