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Simplifying 5x2 + 9x + -20 = 0 Reorder the terms: -20 + 9x + 5x2 = 0 Solving -20 + 9x + 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 + 1.8x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.8x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 1.8x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.8x + x2 = 0 + 4 1.8x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.8x + x2 = 4 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = 4 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 4 + 0.81 Combine like terms: 4 + 0.81 = 4.81 0.81 + 1.8x + x2 = 4.81 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 4.81 Calculate the square root of the right side: 2.19317122 Break this problem into two subproblems by setting (x + 0.9) equal to 2.19317122 and -2.19317122.Subproblem 1
x + 0.9 = 2.19317122 Simplifying x + 0.9 = 2.19317122 Reorder the terms: 0.9 + x = 2.19317122 Solving 0.9 + x = 2.19317122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 2.19317122 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 2.19317122 + -0.9 x = 2.19317122 + -0.9 Combine like terms: 2.19317122 + -0.9 = 1.29317122 x = 1.29317122 Simplifying x = 1.29317122Subproblem 2
x + 0.9 = -2.19317122 Simplifying x + 0.9 = -2.19317122 Reorder the terms: 0.9 + x = -2.19317122 Solving 0.9 + x = -2.19317122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -2.19317122 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -2.19317122 + -0.9 x = -2.19317122 + -0.9 Combine like terms: -2.19317122 + -0.9 = -3.09317122 x = -3.09317122 Simplifying x = -3.09317122Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.29317122, -3.09317122}
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