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Simplifying 3x2 + -69x + -51 = 0 Reorder the terms: -51 + -69x + 3x2 = 0 Solving -51 + -69x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-17 + -23x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-17 + -23x + x2)' equal to zero and attempt to solve: Simplifying -17 + -23x + x2 = 0 Solving -17 + -23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -23x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -23x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -23x + x2 = 0 + 17 -23x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -23x + x2 = 17 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = 17 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 17 + 132.25 Combine like terms: 17 + 132.25 = 149.25 132.25 + -23x + x2 = 149.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 149.25 Calculate the square root of the right side: 12.216791723 Break this problem into two subproblems by setting (x + -11.5) equal to 12.216791723 and -12.216791723.Subproblem 1
x + -11.5 = 12.216791723 Simplifying x + -11.5 = 12.216791723 Reorder the terms: -11.5 + x = 12.216791723 Solving -11.5 + x = 12.216791723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 12.216791723 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 12.216791723 + 11.5 x = 12.216791723 + 11.5 Combine like terms: 12.216791723 + 11.5 = 23.716791723 x = 23.716791723 Simplifying x = 23.716791723Subproblem 2
x + -11.5 = -12.216791723 Simplifying x + -11.5 = -12.216791723 Reorder the terms: -11.5 + x = -12.216791723 Solving -11.5 + x = -12.216791723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -12.216791723 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -12.216791723 + 11.5 x = -12.216791723 + 11.5 Combine like terms: -12.216791723 + 11.5 = -0.716791723 x = -0.716791723 Simplifying x = -0.716791723Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.716791723, -0.716791723}Solution
x = {23.716791723, -0.716791723}
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