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Simplifying 5x2 + -9x + -45 = 0 Reorder the terms: -45 + -9x + 5x2 = 0 Solving -45 + -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'. -9 + -1.8x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -1.8x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -1.8x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1.8x + x2 = 0 + 9 -1.8x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -1.8x + x2 = 9 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 = 9 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 9 + 0.81 Combine like terms: 9 + 0.81 = 9.81 0.81 + -1.8x + x2 = 9.81 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 9.81 Calculate the square root of the right side: 3.132091953 Break this problem into two subproblems by setting (x + -0.9) equal to 3.132091953 and -3.132091953.Subproblem 1
x + -0.9 = 3.132091953 Simplifying x + -0.9 = 3.132091953 Reorder the terms: -0.9 + x = 3.132091953 Solving -0.9 + x = 3.132091953 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 = 3.132091953 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 3.132091953 + 0.9 x = 3.132091953 + 0.9 Combine like terms: 3.132091953 + 0.9 = 4.032091953 x = 4.032091953 Simplifying x = 4.032091953Subproblem 2
x + -0.9 = -3.132091953 Simplifying x + -0.9 = -3.132091953 Reorder the terms: -0.9 + x = -3.132091953 Solving -0.9 + x = -3.132091953 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 = -3.132091953 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -3.132091953 + 0.9 x = -3.132091953 + 0.9 Combine like terms: -3.132091953 + 0.9 = -2.232091953 x = -2.232091953 Simplifying x = -2.232091953Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.032091953, -2.232091953}
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