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Simplifying 10x2 + -43x + -19 = 0 Reorder the terms: -19 + -43x + 10x2 = 0 Solving -19 + -43x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.9 + -4.3x + x2 = 0 Move the constant term to the right: Add '1.9' to each side of the equation. -1.9 + -4.3x + 1.9 + x2 = 0 + 1.9 Reorder the terms: -1.9 + 1.9 + -4.3x + x2 = 0 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + -4.3x + x2 = 0 + 1.9 -4.3x + x2 = 0 + 1.9 Combine like terms: 0 + 1.9 = 1.9 -4.3x + x2 = 1.9 The x term is -4.3x. Take half its coefficient (-2.15). Square it (4.6225) and add it to both sides. Add '4.6225' to each side of the equation. -4.3x + 4.6225 + x2 = 1.9 + 4.6225 Reorder the terms: 4.6225 + -4.3x + x2 = 1.9 + 4.6225 Combine like terms: 1.9 + 4.6225 = 6.5225 4.6225 + -4.3x + x2 = 6.5225 Factor a perfect square on the left side: (x + -2.15)(x + -2.15) = 6.5225 Calculate the square root of the right side: 2.553918558 Break this problem into two subproblems by setting (x + -2.15) equal to 2.553918558 and -2.553918558.Subproblem 1
x + -2.15 = 2.553918558 Simplifying x + -2.15 = 2.553918558 Reorder the terms: -2.15 + x = 2.553918558 Solving -2.15 + x = 2.553918558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.15' to each side of the equation. -2.15 + 2.15 + x = 2.553918558 + 2.15 Combine like terms: -2.15 + 2.15 = 0.00 0.00 + x = 2.553918558 + 2.15 x = 2.553918558 + 2.15 Combine like terms: 2.553918558 + 2.15 = 4.703918558 x = 4.703918558 Simplifying x = 4.703918558Subproblem 2
x + -2.15 = -2.553918558 Simplifying x + -2.15 = -2.553918558 Reorder the terms: -2.15 + x = -2.553918558 Solving -2.15 + x = -2.553918558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.15' to each side of the equation. -2.15 + 2.15 + x = -2.553918558 + 2.15 Combine like terms: -2.15 + 2.15 = 0.00 0.00 + x = -2.553918558 + 2.15 x = -2.553918558 + 2.15 Combine like terms: -2.553918558 + 2.15 = -0.403918558 x = -0.403918558 Simplifying x = -0.403918558Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.703918558, -0.403918558}
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