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Simplifying 4x2 + -66x + 100 = 0 Reorder the terms: 100 + -66x + 4x2 = 0 Solving 100 + -66x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(50 + -33x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + -33x + 2x2)' equal to zero and attempt to solve: Simplifying 50 + -33x + 2x2 = 0 Solving 50 + -33x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 25 + -16.5x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -16.5x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -16.5x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -16.5x + x2 = 0 + -25 -16.5x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -16.5x + x2 = -25 The x term is -16.5x. Take half its coefficient (-8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. -16.5x + 68.0625 + x2 = -25 + 68.0625 Reorder the terms: 68.0625 + -16.5x + x2 = -25 + 68.0625 Combine like terms: -25 + 68.0625 = 43.0625 68.0625 + -16.5x + x2 = 43.0625 Factor a perfect square on the left side: (x + -8.25)(x + -8.25) = 43.0625 Calculate the square root of the right side: 6.562202374 Break this problem into two subproblems by setting (x + -8.25) equal to 6.562202374 and -6.562202374.Subproblem 1
x + -8.25 = 6.562202374 Simplifying x + -8.25 = 6.562202374 Reorder the terms: -8.25 + x = 6.562202374 Solving -8.25 + x = 6.562202374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = 6.562202374 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = 6.562202374 + 8.25 x = 6.562202374 + 8.25 Combine like terms: 6.562202374 + 8.25 = 14.812202374 x = 14.812202374 Simplifying x = 14.812202374Subproblem 2
x + -8.25 = -6.562202374 Simplifying x + -8.25 = -6.562202374 Reorder the terms: -8.25 + x = -6.562202374 Solving -8.25 + x = -6.562202374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = -6.562202374 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = -6.562202374 + 8.25 x = -6.562202374 + 8.25 Combine like terms: -6.562202374 + 8.25 = 1.687797626 x = 1.687797626 Simplifying x = 1.687797626Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.812202374, 1.687797626}Solution
x = {14.812202374, 1.687797626}
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