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Simplifying 4x2 + 90x + -100 = 0 Reorder the terms: -100 + 90x + 4x2 = 0 Solving -100 + 90x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 45x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 45x + 2x2)' equal to zero and attempt to solve: Simplifying -50 + 45x + 2x2 = 0 Solving -50 + 45x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25 + 22.5x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 22.5x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 22.5x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 22.5x + x2 = 0 + 25 22.5x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 22.5x + x2 = 25 The x term is 22.5x. Take half its coefficient (11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. 22.5x + 126.5625 + x2 = 25 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = 25 + 126.5625 Combine like terms: 25 + 126.5625 = 151.5625 126.5625 + 22.5x + x2 = 151.5625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 151.5625 Calculate the square root of the right side: 12.311072252 Break this problem into two subproblems by setting (x + 11.25) equal to 12.311072252 and -12.311072252.Subproblem 1
x + 11.25 = 12.311072252 Simplifying x + 11.25 = 12.311072252 Reorder the terms: 11.25 + x = 12.311072252 Solving 11.25 + x = 12.311072252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = 12.311072252 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 12.311072252 + -11.25 x = 12.311072252 + -11.25 Combine like terms: 12.311072252 + -11.25 = 1.061072252 x = 1.061072252 Simplifying x = 1.061072252Subproblem 2
x + 11.25 = -12.311072252 Simplifying x + 11.25 = -12.311072252 Reorder the terms: 11.25 + x = -12.311072252 Solving 11.25 + x = -12.311072252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.25' to each side of the equation. 11.25 + -11.25 + x = -12.311072252 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -12.311072252 + -11.25 x = -12.311072252 + -11.25 Combine like terms: -12.311072252 + -11.25 = -23.561072252 x = -23.561072252 Simplifying x = -23.561072252Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.061072252, -23.561072252}Solution
x = {1.061072252, -23.561072252}
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