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Simplifying x2 + -1.8x + -36 = 0 Reorder the terms: -36 + -1.8x + x2 = 0 Solving -36 + -1.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -1.8x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -1.8x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -1.8x + x2 = 0 + 36 -1.8x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -1.8x + x2 = 36 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 = 36 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 36 + 0.81 Combine like terms: 36 + 0.81 = 36.81 0.81 + -1.8x + x2 = 36.81 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 36.81 Calculate the square root of the right side: 6.067124525 Break this problem into two subproblems by setting (x + -0.9) equal to 6.067124525 and -6.067124525.Subproblem 1
x + -0.9 = 6.067124525 Simplifying x + -0.9 = 6.067124525 Reorder the terms: -0.9 + x = 6.067124525 Solving -0.9 + x = 6.067124525 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 = 6.067124525 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 6.067124525 + 0.9 x = 6.067124525 + 0.9 Combine like terms: 6.067124525 + 0.9 = 6.967124525 x = 6.967124525 Simplifying x = 6.967124525Subproblem 2
x + -0.9 = -6.067124525 Simplifying x + -0.9 = -6.067124525 Reorder the terms: -0.9 + x = -6.067124525 Solving -0.9 + x = -6.067124525 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 = -6.067124525 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -6.067124525 + 0.9 x = -6.067124525 + 0.9 Combine like terms: -6.067124525 + 0.9 = -5.167124525 x = -5.167124525 Simplifying x = -5.167124525Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.967124525, -5.167124525}
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