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Simplifying 3x2 + 72x + 210 = 0 Reorder the terms: 210 + 72x + 3x2 = 0 Solving 210 + 72x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(70 + 24x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(70 + 24x + x2)' equal to zero and attempt to solve: Simplifying 70 + 24x + x2 = 0 Solving 70 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + 24x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + 24x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + 24x + x2 = 0 + -70 24x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 24x + x2 = -70 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -70 + 144 Reorder the terms: 144 + 24x + x2 = -70 + 144 Combine like terms: -70 + 144 = 74 144 + 24x + x2 = 74 Factor a perfect square on the left side: (x + 12)(x + 12) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (x + 12) equal to 8.602325267 and -8.602325267.Subproblem 1
x + 12 = 8.602325267 Simplifying x + 12 = 8.602325267 Reorder the terms: 12 + x = 8.602325267 Solving 12 + x = 8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 8.602325267 + -12 Combine like terms: 12 + -12 = 0 0 + x = 8.602325267 + -12 x = 8.602325267 + -12 Combine like terms: 8.602325267 + -12 = -3.397674733 x = -3.397674733 Simplifying x = -3.397674733Subproblem 2
x + 12 = -8.602325267 Simplifying x + 12 = -8.602325267 Reorder the terms: 12 + x = -8.602325267 Solving 12 + x = -8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -8.602325267 + -12 Combine like terms: 12 + -12 = 0 0 + x = -8.602325267 + -12 x = -8.602325267 + -12 Combine like terms: -8.602325267 + -12 = -20.602325267 x = -20.602325267 Simplifying x = -20.602325267Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.397674733, -20.602325267}Solution
x = {-3.397674733, -20.602325267}
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