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Simplifying x2 + 12x = 0.32 Reorder the terms: 12x + x2 = 0.32 Solving 12x + x2 = 0.32 Solving for variable 'x'. Reorder the terms: -0.32 + 12x + x2 = 0.32 + -0.32 Combine like terms: 0.32 + -0.32 = 0.00 -0.32 + 12x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.32' to each side of the equation. -0.32 + 12x + 0.32 + x2 = 0.00 + 0.32 Reorder the terms: -0.32 + 0.32 + 12x + x2 = 0.00 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + 12x + x2 = 0.00 + 0.32 12x + x2 = 0.00 + 0.32 Combine like terms: 0.00 + 0.32 = 0.32 12x + x2 = 0.32 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 0.32 + 36 Reorder the terms: 36 + 12x + x2 = 0.32 + 36 Combine like terms: 0.32 + 36 = 36.32 36 + 12x + x2 = 36.32 Factor a perfect square on the left side: (x + 6)(x + 6) = 36.32 Calculate the square root of the right side: 6.026607669 Break this problem into two subproblems by setting (x + 6) equal to 6.026607669 and -6.026607669.Subproblem 1
x + 6 = 6.026607669 Simplifying x + 6 = 6.026607669 Reorder the terms: 6 + x = 6.026607669 Solving 6 + x = 6.026607669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.026607669 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.026607669 + -6 x = 6.026607669 + -6 Combine like terms: 6.026607669 + -6 = 0.026607669 x = 0.026607669 Simplifying x = 0.026607669Subproblem 2
x + 6 = -6.026607669 Simplifying x + 6 = -6.026607669 Reorder the terms: 6 + x = -6.026607669 Solving 6 + x = -6.026607669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.026607669 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.026607669 + -6 x = -6.026607669 + -6 Combine like terms: -6.026607669 + -6 = -12.026607669 x = -12.026607669 Simplifying x = -12.026607669Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.026607669, -12.026607669}
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