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Simplifying 5x2 + 9x = 20.05 Reorder the terms: 9x + 5x2 = 20.05 Solving 9x + 5x2 = 20.05 Solving for variable 'x'. Reorder the terms: -20.05 + 9x + 5x2 = 20.05 + -20.05 Combine like terms: 20.05 + -20.05 = 0.00 -20.05 + 9x + 5x2 = 0.00 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.01 + 1.8x + x2 = 0.00 Move the constant term to the right: Add '4.01' to each side of the equation. -4.01 + 1.8x + 4.01 + x2 = 0.00 + 4.01 Reorder the terms: -4.01 + 4.01 + 1.8x + x2 = 0.00 + 4.01 Combine like terms: -4.01 + 4.01 = 0.00 0.00 + 1.8x + x2 = 0.00 + 4.01 1.8x + x2 = 0.00 + 4.01 Combine like terms: 0.00 + 4.01 = 4.01 1.8x + x2 = 4.01 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 = 4.01 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 4.01 + 0.81 Combine like terms: 4.01 + 0.81 = 4.82 0.81 + 1.8x + x2 = 4.82 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 4.82 Calculate the square root of the right side: 2.19544984 Break this problem into two subproblems by setting (x + 0.9) equal to 2.19544984 and -2.19544984.Subproblem 1
x + 0.9 = 2.19544984 Simplifying x + 0.9 = 2.19544984 Reorder the terms: 0.9 + x = 2.19544984 Solving 0.9 + x = 2.19544984 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 = 2.19544984 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 2.19544984 + -0.9 x = 2.19544984 + -0.9 Combine like terms: 2.19544984 + -0.9 = 1.29544984 x = 1.29544984 Simplifying x = 1.29544984Subproblem 2
x + 0.9 = -2.19544984 Simplifying x + 0.9 = -2.19544984 Reorder the terms: 0.9 + x = -2.19544984 Solving 0.9 + x = -2.19544984 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 = -2.19544984 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -2.19544984 + -0.9 x = -2.19544984 + -0.9 Combine like terms: -2.19544984 + -0.9 = -3.09544984 x = -3.09544984 Simplifying x = -3.09544984Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.29544984, -3.09544984}
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