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Simplifying 40x2 + 240x + 90 = 0 Reorder the terms: 90 + 240x + 40x2 = 0 Solving 90 + 240x + 40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(9 + 24x + 4x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(9 + 24x + 4x2)' equal to zero and attempt to solve: Simplifying 9 + 24x + 4x2 = 0 Solving 9 + 24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 6x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 6x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 6x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 6x + x2 = 0 + -2.25 6x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 6x + x2 = -2.25 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -2.25 + 9 Reorder the terms: 9 + 6x + x2 = -2.25 + 9 Combine like terms: -2.25 + 9 = 6.75 9 + 6x + x2 = 6.75 Factor a perfect square on the left side: (x + 3)(x + 3) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + 3) equal to 2.598076211 and -2.598076211.Subproblem 1
x + 3 = 2.598076211 Simplifying x + 3 = 2.598076211 Reorder the terms: 3 + x = 2.598076211 Solving 3 + x = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.598076211 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.598076211 + -3 x = 2.598076211 + -3 Combine like terms: 2.598076211 + -3 = -0.401923789 x = -0.401923789 Simplifying x = -0.401923789Subproblem 2
x + 3 = -2.598076211 Simplifying x + 3 = -2.598076211 Reorder the terms: 3 + x = -2.598076211 Solving 3 + x = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.598076211 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.598076211 + -3 x = -2.598076211 + -3 Combine like terms: -2.598076211 + -3 = -5.598076211 x = -5.598076211 Simplifying x = -5.598076211Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.401923789, -5.598076211}Solution
x = {-0.401923789, -5.598076211}
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