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Simplifying 3x2 + 30x = -21 Reorder the terms: 30x + 3x2 = -21 Solving 30x + 3x2 = -21 Solving for variable 'x'. Reorder the terms: 21 + 30x + 3x2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + 30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(7 + 10x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + 10x + x2)' equal to zero and attempt to solve: Simplifying 7 + 10x + x2 = 0 Solving 7 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 10x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 10x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 10x + x2 = 0 + -7 10x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 10x + x2 = -7 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 = -7 + 25 Reorder the terms: 25 + 10x + x2 = -7 + 25 Combine like terms: -7 + 25 = 18 25 + 10x + x2 = 18 Factor a perfect square on the left side: (x + 5)(x + 5) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + 5) equal to 4.242640687 and -4.242640687.Subproblem 1
x + 5 = 4.242640687 Simplifying x + 5 = 4.242640687 Reorder the terms: 5 + x = 4.242640687 Solving 5 + x = 4.242640687 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 = 4.242640687 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.242640687 + -5 x = 4.242640687 + -5 Combine like terms: 4.242640687 + -5 = -0.757359313 x = -0.757359313 Simplifying x = -0.757359313Subproblem 2
x + 5 = -4.242640687 Simplifying x + 5 = -4.242640687 Reorder the terms: 5 + x = -4.242640687 Solving 5 + x = -4.242640687 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 = -4.242640687 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.242640687 + -5 x = -4.242640687 + -5 Combine like terms: -4.242640687 + -5 = -9.242640687 x = -9.242640687 Simplifying x = -9.242640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.757359313, -9.242640687}Solution
x = {-0.757359313, -9.242640687}
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