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Simplifying 4x2 + -24x + -76 = 0 Reorder the terms: -76 + -24x + 4x2 = 0 Solving -76 + -24x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-19 + -6x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-19 + -6x + x2)' equal to zero and attempt to solve: Simplifying -19 + -6x + x2 = 0 Solving -19 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -6x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -6x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -6x + x2 = 0 + 19 -6x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -6x + x2 = 19 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 19 + 9 Reorder the terms: 9 + -6x + x2 = 19 + 9 Combine like terms: 19 + 9 = 28 9 + -6x + x2 = 28 Factor a perfect square on the left side: (x + -3)(x + -3) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + -3) equal to 5.291502622 and -5.291502622.Subproblem 1
x + -3 = 5.291502622 Simplifying x + -3 = 5.291502622 Reorder the terms: -3 + x = 5.291502622 Solving -3 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.291502622 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.291502622 + 3 x = 5.291502622 + 3 Combine like terms: 5.291502622 + 3 = 8.291502622 x = 8.291502622 Simplifying x = 8.291502622Subproblem 2
x + -3 = -5.291502622 Simplifying x + -3 = -5.291502622 Reorder the terms: -3 + x = -5.291502622 Solving -3 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.291502622 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.291502622 + 3 x = -5.291502622 + 3 Combine like terms: -5.291502622 + 3 = -2.291502622 x = -2.291502622 Simplifying x = -2.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.291502622, -2.291502622}Solution
x = {8.291502622, -2.291502622}
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