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Simplifying 2x2 + 56x + -36 = 0 Reorder the terms: -36 + 56x + 2x2 = 0 Solving -36 + 56x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 28x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + 28x + x2)' equal to zero and attempt to solve: Simplifying -18 + 28x + x2 = 0 Solving -18 + 28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 28x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 28x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 28x + x2 = 0 + 18 28x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 28x + x2 = 18 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = 18 + 196 Reorder the terms: 196 + 28x + x2 = 18 + 196 Combine like terms: 18 + 196 = 214 196 + 28x + x2 = 214 Factor a perfect square on the left side: (x + 14)(x + 14) = 214 Calculate the square root of the right side: 14.628738838 Break this problem into two subproblems by setting (x + 14) equal to 14.628738838 and -14.628738838.Subproblem 1
x + 14 = 14.628738838 Simplifying x + 14 = 14.628738838 Reorder the terms: 14 + x = 14.628738838 Solving 14 + x = 14.628738838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 14.628738838 + -14 Combine like terms: 14 + -14 = 0 0 + x = 14.628738838 + -14 x = 14.628738838 + -14 Combine like terms: 14.628738838 + -14 = 0.628738838 x = 0.628738838 Simplifying x = 0.628738838Subproblem 2
x + 14 = -14.628738838 Simplifying x + 14 = -14.628738838 Reorder the terms: 14 + x = -14.628738838 Solving 14 + x = -14.628738838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -14.628738838 + -14 Combine like terms: 14 + -14 = 0 0 + x = -14.628738838 + -14 x = -14.628738838 + -14 Combine like terms: -14.628738838 + -14 = -28.628738838 x = -28.628738838 Simplifying x = -28.628738838Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.628738838, -28.628738838}Solution
x = {0.628738838, -28.628738838}
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