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Simplifying 22x2 + 4x + -72 = 0 Reorder the terms: -72 + 4x + 22x2 = 0 Solving -72 + 4x + 22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + 2x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + 2x + 11x2)' equal to zero and attempt to solve: Simplifying -36 + 2x + 11x2 = 0 Solving -36 + 2x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -3.272727273 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '3.272727273' to each side of the equation. -3.272727273 + 0.1818181818x + 3.272727273 + x2 = 0 + 3.272727273 Reorder the terms: -3.272727273 + 3.272727273 + 0.1818181818x + x2 = 0 + 3.272727273 Combine like terms: -3.272727273 + 3.272727273 = 0.000000000 0.000000000 + 0.1818181818x + x2 = 0 + 3.272727273 0.1818181818x + x2 = 0 + 3.272727273 Combine like terms: 0 + 3.272727273 = 3.272727273 0.1818181818x + x2 = 3.272727273 The x term is 0.1818181818x. Take half its coefficient (0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. 0.1818181818x + 0.008264462808 + x2 = 3.272727273 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 3.272727273 + 0.008264462808 Combine like terms: 3.272727273 + 0.008264462808 = 3.280991735808 0.008264462808 + 0.1818181818x + x2 = 3.280991735808 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 3.280991735808 Calculate the square root of the right side: 1.811350804 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 1.811350804 and -1.811350804.Subproblem 1
x + 0.0909090909 = 1.811350804 Simplifying x + 0.0909090909 = 1.811350804 Reorder the terms: 0.0909090909 + x = 1.811350804 Solving 0.0909090909 + x = 1.811350804 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = 1.811350804 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 1.811350804 + -0.0909090909 x = 1.811350804 + -0.0909090909 Combine like terms: 1.811350804 + -0.0909090909 = 1.7204417131 x = 1.7204417131 Simplifying x = 1.7204417131Subproblem 2
x + 0.0909090909 = -1.811350804 Simplifying x + 0.0909090909 = -1.811350804 Reorder the terms: 0.0909090909 + x = -1.811350804 Solving 0.0909090909 + x = -1.811350804 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = -1.811350804 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -1.811350804 + -0.0909090909 x = -1.811350804 + -0.0909090909 Combine like terms: -1.811350804 + -0.0909090909 = -1.9022598949 x = -1.9022598949 Simplifying x = -1.9022598949Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7204417131, -1.9022598949}Solution
x = {1.7204417131, -1.9022598949}
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