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Simplifying 5x2 + 9x = 196 Reorder the terms: 9x + 5x2 = 196 Solving 9x + 5x2 = 196 Solving for variable 'x'. Reorder the terms: -196 + 9x + 5x2 = 196 + -196 Combine like terms: 196 + -196 = 0 -196 + 9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -39.2 + 1.8x + x2 = 0 Move the constant term to the right: Add '39.2' to each side of the equation. -39.2 + 1.8x + 39.2 + x2 = 0 + 39.2 Reorder the terms: -39.2 + 39.2 + 1.8x + x2 = 0 + 39.2 Combine like terms: -39.2 + 39.2 = 0.0 0.0 + 1.8x + x2 = 0 + 39.2 1.8x + x2 = 0 + 39.2 Combine like terms: 0 + 39.2 = 39.2 1.8x + x2 = 39.2 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 = 39.2 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 39.2 + 0.81 Combine like terms: 39.2 + 0.81 = 40.01 0.81 + 1.8x + x2 = 40.01 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 40.01 Calculate the square root of the right side: 6.32534584 Break this problem into two subproblems by setting (x + 0.9) equal to 6.32534584 and -6.32534584.Subproblem 1
x + 0.9 = 6.32534584 Simplifying x + 0.9 = 6.32534584 Reorder the terms: 0.9 + x = 6.32534584 Solving 0.9 + x = 6.32534584 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 = 6.32534584 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 6.32534584 + -0.9 x = 6.32534584 + -0.9 Combine like terms: 6.32534584 + -0.9 = 5.42534584 x = 5.42534584 Simplifying x = 5.42534584Subproblem 2
x + 0.9 = -6.32534584 Simplifying x + 0.9 = -6.32534584 Reorder the terms: 0.9 + x = -6.32534584 Solving 0.9 + x = -6.32534584 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 = -6.32534584 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -6.32534584 + -0.9 x = -6.32534584 + -0.9 Combine like terms: -6.32534584 + -0.9 = -7.22534584 x = -7.22534584 Simplifying x = -7.22534584Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.42534584, -7.22534584}
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