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Simplifying 6x2 + -12x + -54 = 0 Reorder the terms: -54 + -12x + 6x2 = 0 Solving -54 + -12x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-9 + -2x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-9 + -2x + x2)' equal to zero and attempt to solve: Simplifying -9 + -2x + x2 = 0 Solving -9 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -2x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -2x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x + x2 = 0 + 9 -2x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2x + x2 = 9 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 9 + 1 Reorder the terms: 1 + -2x + x2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + -2x + x2 = 10 Factor a perfect square on the left side: (x + -1)(x + -1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -1) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -1 = 3.16227766 Simplifying x + -1 = 3.16227766 Reorder the terms: -1 + x = 3.16227766 Solving -1 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.16227766 + 1 x = 3.16227766 + 1 Combine like terms: 3.16227766 + 1 = 4.16227766 x = 4.16227766 Simplifying x = 4.16227766Subproblem 2
x + -1 = -3.16227766 Simplifying x + -1 = -3.16227766 Reorder the terms: -1 + x = -3.16227766 Solving -1 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.16227766 + 1 x = -3.16227766 + 1 Combine like terms: -3.16227766 + 1 = -2.16227766 x = -2.16227766 Simplifying x = -2.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.16227766, -2.16227766}Solution
x = {4.16227766, -2.16227766}
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