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Simplifying -5x2 + 44x + 3 = 0 Reorder the terms: 3 + 44x + -5x2 = 0 Solving 3 + 44x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.6 + -8.8x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -8.8x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -8.8x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -8.8x + x2 = 0 + 0.6 -8.8x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -8.8x + x2 = 0.6 The x term is -8.8x. Take half its coefficient (-4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. -8.8x + 19.36 + x2 = 0.6 + 19.36 Reorder the terms: 19.36 + -8.8x + x2 = 0.6 + 19.36 Combine like terms: 0.6 + 19.36 = 19.96 19.36 + -8.8x + x2 = 19.96 Factor a perfect square on the left side: (x + -4.4)(x + -4.4) = 19.96 Calculate the square root of the right side: 4.467661581 Break this problem into two subproblems by setting (x + -4.4) equal to 4.467661581 and -4.467661581.Subproblem 1
x + -4.4 = 4.467661581 Simplifying x + -4.4 = 4.467661581 Reorder the terms: -4.4 + x = 4.467661581 Solving -4.4 + x = 4.467661581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = 4.467661581 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = 4.467661581 + 4.4 x = 4.467661581 + 4.4 Combine like terms: 4.467661581 + 4.4 = 8.867661581 x = 8.867661581 Simplifying x = 8.867661581Subproblem 2
x + -4.4 = -4.467661581 Simplifying x + -4.4 = -4.467661581 Reorder the terms: -4.4 + x = -4.467661581 Solving -4.4 + x = -4.467661581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = -4.467661581 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = -4.467661581 + 4.4 x = -4.467661581 + 4.4 Combine like terms: -4.467661581 + 4.4 = -0.067661581 x = -0.067661581 Simplifying x = -0.067661581Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.867661581, -0.067661581}
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