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Simplifying 5x2 + -29x + -20 = 0 Reorder the terms: -20 + -29x + 5x2 = 0 Solving -20 + -29x + 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'. -4 + -5.8x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -5.8x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -5.8x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5.8x + x2 = 0 + 4 -5.8x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -5.8x + x2 = 4 The x term is -5.8x. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8x + 8.41 + x2 = 4 + 8.41 Reorder the terms: 8.41 + -5.8x + x2 = 4 + 8.41 Combine like terms: 4 + 8.41 = 12.41 8.41 + -5.8x + x2 = 12.41 Factor a perfect square on the left side: (x + -2.9)(x + -2.9) = 12.41 Calculate the square root of the right side: 3.522782991 Break this problem into two subproblems by setting (x + -2.9) equal to 3.522782991 and -3.522782991.Subproblem 1
x + -2.9 = 3.522782991 Simplifying x + -2.9 = 3.522782991 Reorder the terms: -2.9 + x = 3.522782991 Solving -2.9 + x = 3.522782991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = 3.522782991 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = 3.522782991 + 2.9 x = 3.522782991 + 2.9 Combine like terms: 3.522782991 + 2.9 = 6.422782991 x = 6.422782991 Simplifying x = 6.422782991Subproblem 2
x + -2.9 = -3.522782991 Simplifying x + -2.9 = -3.522782991 Reorder the terms: -2.9 + x = -3.522782991 Solving -2.9 + x = -3.522782991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = -3.522782991 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = -3.522782991 + 2.9 x = -3.522782991 + 2.9 Combine like terms: -3.522782991 + 2.9 = -0.622782991 x = -0.622782991 Simplifying x = -0.622782991Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.422782991, -0.622782991}
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