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Simplifying 5x2 + 9x + -165 = 0 Reorder the terms: -165 + 9x + 5x2 = 0 Solving -165 + 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'. -33 + 1.8x + x2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + 1.8x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 1.8x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 1.8x + x2 = 0 + 33 1.8x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 1.8x + x2 = 33 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 = 33 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 33 + 0.81 Combine like terms: 33 + 0.81 = 33.81 0.81 + 1.8x + x2 = 33.81 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 33.81 Calculate the square root of the right side: 5.814636704 Break this problem into two subproblems by setting (x + 0.9) equal to 5.814636704 and -5.814636704.Subproblem 1
x + 0.9 = 5.814636704 Simplifying x + 0.9 = 5.814636704 Reorder the terms: 0.9 + x = 5.814636704 Solving 0.9 + x = 5.814636704 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 = 5.814636704 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 5.814636704 + -0.9 x = 5.814636704 + -0.9 Combine like terms: 5.814636704 + -0.9 = 4.914636704 x = 4.914636704 Simplifying x = 4.914636704Subproblem 2
x + 0.9 = -5.814636704 Simplifying x + 0.9 = -5.814636704 Reorder the terms: 0.9 + x = -5.814636704 Solving 0.9 + x = -5.814636704 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 = -5.814636704 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -5.814636704 + -0.9 x = -5.814636704 + -0.9 Combine like terms: -5.814636704 + -0.9 = -6.714636704 x = -6.714636704 Simplifying x = -6.714636704Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.914636704, -6.714636704}
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