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Simplifying 4x2 + -14x + -24 = 0 Reorder the terms: -24 + -14x + 4x2 = 0 Solving -24 + -14x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -7x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -7x + 2x2)' equal to zero and attempt to solve: Simplifying -12 + -7x + 2x2 = 0 Solving -12 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + -3.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -3.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -3.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -3.5x + x2 = 0 + 6 -3.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -3.5x + x2 = 6 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 6 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 6 + 3.0625 Combine like terms: 6 + 3.0625 = 9.0625 3.0625 + -3.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + -1.75) equal to 3.010398645 and -3.010398645.Subproblem 1
x + -1.75 = 3.010398645 Simplifying x + -1.75 = 3.010398645 Reorder the terms: -1.75 + x = 3.010398645 Solving -1.75 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.010398645 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.010398645 + 1.75 x = 3.010398645 + 1.75 Combine like terms: 3.010398645 + 1.75 = 4.760398645 x = 4.760398645 Simplifying x = 4.760398645Subproblem 2
x + -1.75 = -3.010398645 Simplifying x + -1.75 = -3.010398645 Reorder the terms: -1.75 + x = -3.010398645 Solving -1.75 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.010398645 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.010398645 + 1.75 x = -3.010398645 + 1.75 Combine like terms: -3.010398645 + 1.75 = -1.260398645 x = -1.260398645 Simplifying x = -1.260398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.760398645, -1.260398645}Solution
x = {4.760398645, -1.260398645}
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