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Simplifying x2 + 10.8x + 0.6 = 0 Reorder the terms: 0.6 + 10.8x + x2 = 0 Solving 0.6 + 10.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 10.8x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 10.8x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 10.8x + x2 = 0 + -0.6 10.8x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 10.8x + x2 = -0.6 The x term is 10.8x. Take half its coefficient (5.4). Square it (29.16) and add it to both sides. Add '29.16' to each side of the equation. 10.8x + 29.16 + x2 = -0.6 + 29.16 Reorder the terms: 29.16 + 10.8x + x2 = -0.6 + 29.16 Combine like terms: -0.6 + 29.16 = 28.56 29.16 + 10.8x + x2 = 28.56 Factor a perfect square on the left side: (x + 5.4)(x + 5.4) = 28.56 Calculate the square root of the right side: 5.344155686 Break this problem into two subproblems by setting (x + 5.4) equal to 5.344155686 and -5.344155686.Subproblem 1
x + 5.4 = 5.344155686 Simplifying x + 5.4 = 5.344155686 Reorder the terms: 5.4 + x = 5.344155686 Solving 5.4 + x = 5.344155686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.4' to each side of the equation. 5.4 + -5.4 + x = 5.344155686 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + x = 5.344155686 + -5.4 x = 5.344155686 + -5.4 Combine like terms: 5.344155686 + -5.4 = -0.055844314 x = -0.055844314 Simplifying x = -0.055844314Subproblem 2
x + 5.4 = -5.344155686 Simplifying x + 5.4 = -5.344155686 Reorder the terms: 5.4 + x = -5.344155686 Solving 5.4 + x = -5.344155686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.4' to each side of the equation. 5.4 + -5.4 + x = -5.344155686 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + x = -5.344155686 + -5.4 x = -5.344155686 + -5.4 Combine like terms: -5.344155686 + -5.4 = -10.744155686 x = -10.744155686 Simplifying x = -10.744155686Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.055844314, -10.744155686}
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