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Simplifying 4x2 + -18.8x + 6.519 = 0 Reorder the terms: 6.519 + -18.8x + 4x2 = 0 Solving 6.519 + -18.8x + 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'. 1.62975 + -4.7x + x2 = 0 Move the constant term to the right: Add '-1.62975' to each side of the equation. 1.62975 + -4.7x + -1.62975 + x2 = 0 + -1.62975 Reorder the terms: 1.62975 + -1.62975 + -4.7x + x2 = 0 + -1.62975 Combine like terms: 1.62975 + -1.62975 = 0.00000 0.00000 + -4.7x + x2 = 0 + -1.62975 -4.7x + x2 = 0 + -1.62975 Combine like terms: 0 + -1.62975 = -1.62975 -4.7x + x2 = -1.62975 The x term is -4.7x. Take half its coefficient (-2.35). Square it (5.5225) and add it to both sides. Add '5.5225' to each side of the equation. -4.7x + 5.5225 + x2 = -1.62975 + 5.5225 Reorder the terms: 5.5225 + -4.7x + x2 = -1.62975 + 5.5225 Combine like terms: -1.62975 + 5.5225 = 3.89275 5.5225 + -4.7x + x2 = 3.89275 Factor a perfect square on the left side: (x + -2.35)(x + -2.35) = 3.89275 Calculate the square root of the right side: 1.973005322 Break this problem into two subproblems by setting (x + -2.35) equal to 1.973005322 and -1.973005322.Subproblem 1
x + -2.35 = 1.973005322 Simplifying x + -2.35 = 1.973005322 Reorder the terms: -2.35 + x = 1.973005322 Solving -2.35 + x = 1.973005322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.35' to each side of the equation. -2.35 + 2.35 + x = 1.973005322 + 2.35 Combine like terms: -2.35 + 2.35 = 0.00 0.00 + x = 1.973005322 + 2.35 x = 1.973005322 + 2.35 Combine like terms: 1.973005322 + 2.35 = 4.323005322 x = 4.323005322 Simplifying x = 4.323005322Subproblem 2
x + -2.35 = -1.973005322 Simplifying x + -2.35 = -1.973005322 Reorder the terms: -2.35 + x = -1.973005322 Solving -2.35 + x = -1.973005322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.35' to each side of the equation. -2.35 + 2.35 + x = -1.973005322 + 2.35 Combine like terms: -2.35 + 2.35 = 0.00 0.00 + x = -1.973005322 + 2.35 x = -1.973005322 + 2.35 Combine like terms: -1.973005322 + 2.35 = 0.376994678 x = 0.376994678 Simplifying x = 0.376994678Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.323005322, 0.376994678}
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