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Simplifying -4x2 + 40x + 12 = 0 Reorder the terms: 12 + 40x + -4x2 = 0 Solving 12 + 40x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + 10x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying 3 + 10x + -1x2 = 0 Solving 3 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -10x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -10x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -10x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -10x + x2 = 0 + 3 -10x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -10x + x2 = 3 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 3 + 25 Reorder the terms: 25 + -10x + x2 = 3 + 25 Combine like terms: 3 + 25 = 28 25 + -10x + x2 = 28 Factor a perfect square on the left side: (x + -5)(x + -5) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + -5) equal to 5.291502622 and -5.291502622.Subproblem 1
x + -5 = 5.291502622 Simplifying x + -5 = 5.291502622 Reorder the terms: -5 + x = 5.291502622 Solving -5 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.291502622 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.291502622 + 5 x = 5.291502622 + 5 Combine like terms: 5.291502622 + 5 = 10.291502622 x = 10.291502622 Simplifying x = 10.291502622Subproblem 2
x + -5 = -5.291502622 Simplifying x + -5 = -5.291502622 Reorder the terms: -5 + x = -5.291502622 Solving -5 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.291502622 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.291502622 + 5 x = -5.291502622 + 5 Combine like terms: -5.291502622 + 5 = -0.291502622 x = -0.291502622 Simplifying x = -0.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.291502622, -0.291502622}Solution
x = {10.291502622, -0.291502622}
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