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Simplifying 5x2 + 50x + 30 = 0 Reorder the terms: 30 + 50x + 5x2 = 0 Solving 30 + 50x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(6 + 10x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6 + 10x + x2)' equal to zero and attempt to solve: Simplifying 6 + 10x + x2 = 0 Solving 6 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 10x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 10x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 10x + x2 = 0 + -6 10x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 10x + x2 = -6 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 = -6 + 25 Reorder the terms: 25 + 10x + x2 = -6 + 25 Combine like terms: -6 + 25 = 19 25 + 10x + x2 = 19 Factor a perfect square on the left side: (x + 5)(x + 5) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 5) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 5 = 4.358898944 Simplifying x + 5 = 4.358898944 Reorder the terms: 5 + x = 4.358898944 Solving 5 + x = 4.358898944 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 = 4.358898944 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.358898944 + -5 x = 4.358898944 + -5 Combine like terms: 4.358898944 + -5 = -0.641101056 x = -0.641101056 Simplifying x = -0.641101056Subproblem 2
x + 5 = -4.358898944 Simplifying x + 5 = -4.358898944 Reorder the terms: 5 + x = -4.358898944 Solving 5 + x = -4.358898944 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 = -4.358898944 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.358898944 + -5 x = -4.358898944 + -5 Combine like terms: -4.358898944 + -5 = -9.358898944 x = -9.358898944 Simplifying x = -9.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.641101056, -9.358898944}Solution
x = {-0.641101056, -9.358898944}
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