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Simplifying 4x2 + 20x + -66 = 0 Reorder the terms: -66 + 20x + 4x2 = 0 Solving -66 + 20x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + 10x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-33 + 10x + 2x2)' equal to zero and attempt to solve: Simplifying -33 + 10x + 2x2 = 0 Solving -33 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + 5x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + 5x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + 5x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + 5x + x2 = 0 + 16.5 5x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 5x + x2 = 16.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 16.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 16.5 + 6.25 Combine like terms: 16.5 + 6.25 = 22.75 6.25 + 5x + x2 = 22.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 22.75 Calculate the square root of the right side: 4.769696007 Break this problem into two subproblems by setting (x + 2.5) equal to 4.769696007 and -4.769696007.Subproblem 1
x + 2.5 = 4.769696007 Simplifying x + 2.5 = 4.769696007 Reorder the terms: 2.5 + x = 4.769696007 Solving 2.5 + x = 4.769696007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 4.769696007 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 4.769696007 + -2.5 x = 4.769696007 + -2.5 Combine like terms: 4.769696007 + -2.5 = 2.269696007 x = 2.269696007 Simplifying x = 2.269696007Subproblem 2
x + 2.5 = -4.769696007 Simplifying x + 2.5 = -4.769696007 Reorder the terms: 2.5 + x = -4.769696007 Solving 2.5 + x = -4.769696007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -4.769696007 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -4.769696007 + -2.5 x = -4.769696007 + -2.5 Combine like terms: -4.769696007 + -2.5 = -7.269696007 x = -7.269696007 Simplifying x = -7.269696007Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.269696007, -7.269696007}Solution
x = {2.269696007, -7.269696007}
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