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Simplifying 4.5x2 + 8.8x + -18 = 0 Reorder the terms: -18 + 8.8x + 4.5x2 = 0 Solving -18 + 8.8x + 4.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.5 the coefficient of the squared term: Divide each side by '4.5'. -4 + 1.955555556x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.955555556x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 1.955555556x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.955555556x + x2 = 0 + 4 1.955555556x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.955555556x + x2 = 4 The x term is 1.955555556x. Take half its coefficient (0.977777778). Square it (0.9560493832) and add it to both sides. Add '0.9560493832' to each side of the equation. 1.955555556x + 0.9560493832 + x2 = 4 + 0.9560493832 Reorder the terms: 0.9560493832 + 1.955555556x + x2 = 4 + 0.9560493832 Combine like terms: 4 + 0.9560493832 = 4.9560493832 0.9560493832 + 1.955555556x + x2 = 4.9560493832 Factor a perfect square on the left side: (x + 0.977777778)(x + 0.977777778) = 4.9560493832 Calculate the square root of the right side: 2.226218629 Break this problem into two subproblems by setting (x + 0.977777778) equal to 2.226218629 and -2.226218629.Subproblem 1
x + 0.977777778 = 2.226218629 Simplifying x + 0.977777778 = 2.226218629 Reorder the terms: 0.977777778 + x = 2.226218629 Solving 0.977777778 + x = 2.226218629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.977777778' to each side of the equation. 0.977777778 + -0.977777778 + x = 2.226218629 + -0.977777778 Combine like terms: 0.977777778 + -0.977777778 = 0.000000000 0.000000000 + x = 2.226218629 + -0.977777778 x = 2.226218629 + -0.977777778 Combine like terms: 2.226218629 + -0.977777778 = 1.248440851 x = 1.248440851 Simplifying x = 1.248440851Subproblem 2
x + 0.977777778 = -2.226218629 Simplifying x + 0.977777778 = -2.226218629 Reorder the terms: 0.977777778 + x = -2.226218629 Solving 0.977777778 + x = -2.226218629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.977777778' to each side of the equation. 0.977777778 + -0.977777778 + x = -2.226218629 + -0.977777778 Combine like terms: 0.977777778 + -0.977777778 = 0.000000000 0.000000000 + x = -2.226218629 + -0.977777778 x = -2.226218629 + -0.977777778 Combine like terms: -2.226218629 + -0.977777778 = -3.203996407 x = -3.203996407 Simplifying x = -3.203996407Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.248440851, -3.203996407}
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