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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 = 101.5625 126.5625 + 22.5x + x2 = 101.5625 Factor a perfect square on the left side: (x + 11.25)(x + 11.25) = 101.5625 Calculate the square root of the right side: 10.077822185 Break this problem into two subproblems by setting (x + 11.25) equal to 10.077822185 and -10.077822185.Subproblem 1
x + 11.25 = 10.077822185 Simplifying x + 11.25 = 10.077822185 Reorder the terms: 11.25 + x = 10.077822185 Solving 11.25 + x = 10.077822185 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 = 10.077822185 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = 10.077822185 + -11.25 x = 10.077822185 + -11.25 Combine like terms: 10.077822185 + -11.25 = -1.172177815 x = -1.172177815 Simplifying x = -1.172177815Subproblem 2
x + 11.25 = -10.077822185 Simplifying x + 11.25 = -10.077822185 Reorder the terms: 11.25 + x = -10.077822185 Solving 11.25 + x = -10.077822185 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 = -10.077822185 + -11.25 Combine like terms: 11.25 + -11.25 = 0.00 0.00 + x = -10.077822185 + -11.25 x = -10.077822185 + -11.25 Combine like terms: -10.077822185 + -11.25 = -21.327822185 x = -21.327822185 Simplifying x = -21.327822185Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.172177815, -21.327822185}Solution
x = {-1.172177815, -21.327822185}
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