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Simplifying 4x2 + 90x = 500 Reorder the terms: 90x + 4x2 = 500 Solving 90x + 4x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + 90x + 4x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 90x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-250 + 45x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-250 + 45x + 2x2)' equal to zero and attempt to solve: Simplifying -250 + 45x + 2x2 = 0 Solving -250 + 45x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -125 + 22.5x + x2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + 22.5x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + 22.5x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 22.5x + x2 = 0 + 125 22.5x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 22.5x + x2 = 125 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 = 125 + 126.5625 Reorder the terms: 126.5625 + 22.5x + x2 = 125 + 126.5625 Combine like terms: 125 + 126.5625 = 251.5625 126.5625 + 22.5x + x2 = 251.5625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 251.5625 Calculate the square root of the right side: 15.860721926 Break this problem into two subproblems by setting (x + 11.25) equal to 15.860721926 and -15.860721926.Subproblem 1
x + 11.25 = 15.860721926 Simplifying x + 11.25 = 15.860721926 Reorder the terms: 11.25 + x = 15.860721926 Solving 11.25 + x = 15.860721926 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 = 15.860721926 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 15.860721926 + -11.25 x = 15.860721926 + -11.25 Combine like terms: 15.860721926 + -11.25 = 4.610721926 x = 4.610721926 Simplifying x = 4.610721926Subproblem 2
x + 11.25 = -15.860721926 Simplifying x + 11.25 = -15.860721926 Reorder the terms: 11.25 + x = -15.860721926 Solving 11.25 + x = -15.860721926 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 = -15.860721926 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -15.860721926 + -11.25 x = -15.860721926 + -11.25 Combine like terms: -15.860721926 + -11.25 = -27.110721926 x = -27.110721926 Simplifying x = -27.110721926Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.610721926, -27.110721926}Solution
x = {4.610721926, -27.110721926}
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