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Simplifying 8x(5x + 9) = 9 Reorder the terms: 8x(9 + 5x) = 9 (9 * 8x + 5x * 8x) = 9 (72x + 40x2) = 9 Solving 72x + 40x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 72x + 40x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 72x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.225 + 1.8x + x2 = 0.0 Move the constant term to the right: Add '0.225' to each side of the equation. -0.225 + 1.8x + 0.225 + x2 = 0.0 + 0.225 Reorder the terms: -0.225 + 0.225 + 1.8x + x2 = 0.0 + 0.225 Combine like terms: -0.225 + 0.225 = 0.000 0.000 + 1.8x + x2 = 0.0 + 0.225 1.8x + x2 = 0.0 + 0.225 Combine like terms: 0.0 + 0.225 = 0.225 1.8x + x2 = 0.225 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 = 0.225 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.225 + 0.81 Combine like terms: 0.225 + 0.81 = 1.035 0.81 + 1.8x + x2 = 1.035 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 1.035 Calculate the square root of the right side: 1.017349497 Break this problem into two subproblems by setting (x + 0.9) equal to 1.017349497 and -1.017349497.Subproblem 1
x + 0.9 = 1.017349497 Simplifying x + 0.9 = 1.017349497 Reorder the terms: 0.9 + x = 1.017349497 Solving 0.9 + x = 1.017349497 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 = 1.017349497 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.017349497 + -0.9 x = 1.017349497 + -0.9 Combine like terms: 1.017349497 + -0.9 = 0.117349497 x = 0.117349497 Simplifying x = 0.117349497Subproblem 2
x + 0.9 = -1.017349497 Simplifying x + 0.9 = -1.017349497 Reorder the terms: 0.9 + x = -1.017349497 Solving 0.9 + x = -1.017349497 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 = -1.017349497 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.017349497 + -0.9 x = -1.017349497 + -0.9 Combine like terms: -1.017349497 + -0.9 = -1.917349497 x = -1.917349497 Simplifying x = -1.917349497Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.117349497, -1.917349497}
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