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Simplifying x2 + -12 = 8(3x) Reorder the terms: -12 + x2 = 8(3x) Remove parenthesis around (3x) -12 + x2 = 8 * 3x Multiply 8 * 3 -12 + x2 = 24x Solving -12 + x2 = 24x Solving for variable 'x'. Reorder the terms: -12 + -24x + x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -12 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -24x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -24x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -24x + x2 = 0 + 12 -24x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -24x + x2 = 12 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 12 + 144 Reorder the terms: 144 + -24x + x2 = 12 + 144 Combine like terms: 12 + 144 = 156 144 + -24x + x2 = 156 Factor a perfect square on the left side: (x + -12)(x + -12) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + -12) equal to 12.489995997 and -12.489995997.Subproblem 1
x + -12 = 12.489995997 Simplifying x + -12 = 12.489995997 Reorder the terms: -12 + x = 12.489995997 Solving -12 + x = 12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 12.489995997 + 12 Combine like terms: -12 + 12 = 0 0 + x = 12.489995997 + 12 x = 12.489995997 + 12 Combine like terms: 12.489995997 + 12 = 24.489995997 x = 24.489995997 Simplifying x = 24.489995997Subproblem 2
x + -12 = -12.489995997 Simplifying x + -12 = -12.489995997 Reorder the terms: -12 + x = -12.489995997 Solving -12 + x = -12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -12.489995997 + 12 Combine like terms: -12 + 12 = 0 0 + x = -12.489995997 + 12 x = -12.489995997 + 12 Combine like terms: -12.489995997 + 12 = -0.489995997 x = -0.489995997 Simplifying x = -0.489995997Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.489995997, -0.489995997}
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