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Simplifying 2x2 + 60x + -22 = 0 Reorder the terms: -22 + 60x + 2x2 = 0 Solving -22 + 60x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 30x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 30x + x2)' equal to zero and attempt to solve: Simplifying -11 + 30x + x2 = 0 Solving -11 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 30x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 30x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 30x + x2 = 0 + 11 30x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 30x + x2 = 11 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 11 + 225 Reorder the terms: 225 + 30x + x2 = 11 + 225 Combine like terms: 11 + 225 = 236 225 + 30x + x2 = 236 Factor a perfect square on the left side: (x + 15)(x + 15) = 236 Calculate the square root of the right side: 15.362291496 Break this problem into two subproblems by setting (x + 15) equal to 15.362291496 and -15.362291496.Subproblem 1
x + 15 = 15.362291496 Simplifying x + 15 = 15.362291496 Reorder the terms: 15 + x = 15.362291496 Solving 15 + x = 15.362291496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 15.362291496 + -15 Combine like terms: 15 + -15 = 0 0 + x = 15.362291496 + -15 x = 15.362291496 + -15 Combine like terms: 15.362291496 + -15 = 0.362291496 x = 0.362291496 Simplifying x = 0.362291496Subproblem 2
x + 15 = -15.362291496 Simplifying x + 15 = -15.362291496 Reorder the terms: 15 + x = -15.362291496 Solving 15 + x = -15.362291496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -15.362291496 + -15 Combine like terms: 15 + -15 = 0 0 + x = -15.362291496 + -15 x = -15.362291496 + -15 Combine like terms: -15.362291496 + -15 = -30.362291496 x = -30.362291496 Simplifying x = -30.362291496Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.362291496, -30.362291496}Solution
x = {0.362291496, -30.362291496}
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