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Simplifying -2x2 + 14x + -6 = 0 Reorder the terms: -6 + 14x + -2x2 = 0 Solving -6 + 14x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 7x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 7x + -1x2)' equal to zero and attempt to solve: Simplifying -3 + 7x + -1x2 = 0 Solving -3 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -7x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -7x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -7x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7x + x2 = 0 + -3 -7x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -7x + x2 = -3 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -3 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -3 + 12.25 Combine like terms: -3 + 12.25 = 9.25 12.25 + -7x + x2 = 9.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + -3.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + -3.5 = 3.041381265 Simplifying x + -3.5 = 3.041381265 Reorder the terms: -3.5 + x = 3.041381265 Solving -3.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.041381265 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.041381265 + 3.5 x = 3.041381265 + 3.5 Combine like terms: 3.041381265 + 3.5 = 6.541381265 x = 6.541381265 Simplifying x = 6.541381265Subproblem 2
x + -3.5 = -3.041381265 Simplifying x + -3.5 = -3.041381265 Reorder the terms: -3.5 + x = -3.041381265 Solving -3.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.041381265 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.041381265 + 3.5 x = -3.041381265 + 3.5 Combine like terms: -3.041381265 + 3.5 = 0.458618735 x = 0.458618735 Simplifying x = 0.458618735Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.541381265, 0.458618735}Solution
x = {6.541381265, 0.458618735}
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