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Simplifying 2x2 + 12x + -140 = 0 Reorder the terms: -140 + 12x + 2x2 = 0 Solving -140 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-70 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-70 + 6x + x2)' equal to zero and attempt to solve: Simplifying -70 + 6x + x2 = 0 Solving -70 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + 6x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 6x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 6x + x2 = 0 + 70 6x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 6x + x2 = 70 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 70 + 9 Reorder the terms: 9 + 6x + x2 = 70 + 9 Combine like terms: 70 + 9 = 79 9 + 6x + x2 = 79 Factor a perfect square on the left side: (x + 3)(x + 3) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + 3) equal to 8.888194417 and -8.888194417.Subproblem 1
x + 3 = 8.888194417 Simplifying x + 3 = 8.888194417 Reorder the terms: 3 + x = 8.888194417 Solving 3 + x = 8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 8.888194417 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.888194417 + -3 x = 8.888194417 + -3 Combine like terms: 8.888194417 + -3 = 5.888194417 x = 5.888194417 Simplifying x = 5.888194417Subproblem 2
x + 3 = -8.888194417 Simplifying x + 3 = -8.888194417 Reorder the terms: 3 + x = -8.888194417 Solving 3 + x = -8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -8.888194417 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.888194417 + -3 x = -8.888194417 + -3 Combine like terms: -8.888194417 + -3 = -11.888194417 x = -11.888194417 Simplifying x = -11.888194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.888194417, -11.888194417}Solution
x = {5.888194417, -11.888194417}
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