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Simplifying 9x2 + -90x + 3 = 0 Reorder the terms: 3 + -90x + 9x2 = 0 Solving 3 + -90x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -30x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -30x + 3x2)' equal to zero and attempt to solve: Simplifying 1 + -30x + 3x2 = 0 Solving 1 + -30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + -10x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -10x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -10x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -10x + x2 = 0 + -0.3333333333 -10x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -10x + x2 = -0.3333333333 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -0.3333333333 + 25 Reorder the terms: 25 + -10x + x2 = -0.3333333333 + 25 Combine like terms: -0.3333333333 + 25 = 24.6666666667 25 + -10x + x2 = 24.6666666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 24.6666666667 Calculate the square root of the right side: 4.966554809 Break this problem into two subproblems by setting (x + -5) equal to 4.966554809 and -4.966554809.Subproblem 1
x + -5 = 4.966554809 Simplifying x + -5 = 4.966554809 Reorder the terms: -5 + x = 4.966554809 Solving -5 + x = 4.966554809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.966554809 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.966554809 + 5 x = 4.966554809 + 5 Combine like terms: 4.966554809 + 5 = 9.966554809 x = 9.966554809 Simplifying x = 9.966554809Subproblem 2
x + -5 = -4.966554809 Simplifying x + -5 = -4.966554809 Reorder the terms: -5 + x = -4.966554809 Solving -5 + x = -4.966554809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.966554809 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.966554809 + 5 x = -4.966554809 + 5 Combine like terms: -4.966554809 + 5 = 0.033445191 x = 0.033445191 Simplifying x = 0.033445191Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.966554809, 0.033445191}Solution
x = {9.966554809, 0.033445191}
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