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Simplifying 12x2 + -18x + -12 = 3 Reorder the terms: -12 + -18x + 12x2 = 3 Solving -12 + -18x + 12x2 = 3 Solving for variable 'x'. Reorder the terms: -12 + -3 + -18x + 12x2 = 3 + -3 Combine like terms: -12 + -3 = -15 -15 + -18x + 12x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -15 + -18x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -6x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -6x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + -6x + 4x2 = 0 Solving -5 + -6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -1.5x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -1.5x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -1.5x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -1.5x + x2 = 0 + 1.25 -1.5x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -1.5x + x2 = 1.25 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 1.25 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 1.25 + 0.5625 Combine like terms: 1.25 + 0.5625 = 1.8125 0.5625 + -1.5x + x2 = 1.8125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (x + -0.75) equal to 1.346291202 and -1.346291202.Subproblem 1
x + -0.75 = 1.346291202 Simplifying x + -0.75 = 1.346291202 Reorder the terms: -0.75 + x = 1.346291202 Solving -0.75 + x = 1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.346291202 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.346291202 + 0.75 x = 1.346291202 + 0.75 Combine like terms: 1.346291202 + 0.75 = 2.096291202 x = 2.096291202 Simplifying x = 2.096291202Subproblem 2
x + -0.75 = -1.346291202 Simplifying x + -0.75 = -1.346291202 Reorder the terms: -0.75 + x = -1.346291202 Solving -0.75 + x = -1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.346291202 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.346291202 + 0.75 x = -1.346291202 + 0.75 Combine like terms: -1.346291202 + 0.75 = -0.596291202 x = -0.596291202 Simplifying x = -0.596291202Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.096291202, -0.596291202}Solution
x = {2.096291202, -0.596291202}
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