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Simplifying 36x2 + 62x = 10 Reorder the terms: 62x + 36x2 = 10 Solving 62x + 36x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 62x + 36x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 62x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 31x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 31x + 18x2)' equal to zero and attempt to solve: Simplifying -5 + 31x + 18x2 = 0 Solving -5 + 31x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2777777778 + 1.722222222x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + 1.722222222x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + 1.722222222x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + 1.722222222x + x2 = 0 + 0.2777777778 1.722222222x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 1.722222222x + x2 = 0.2777777778 The x term is 1.722222222x. Take half its coefficient (0.861111111). Square it (0.7415123455) and add it to both sides. Add '0.7415123455' to each side of the equation. 1.722222222x + 0.7415123455 + x2 = 0.2777777778 + 0.7415123455 Reorder the terms: 0.7415123455 + 1.722222222x + x2 = 0.2777777778 + 0.7415123455 Combine like terms: 0.2777777778 + 0.7415123455 = 1.0192901233 0.7415123455 + 1.722222222x + x2 = 1.0192901233 Factor a perfect square on the left side: (x + 0.861111111)(x + 0.861111111) = 1.0192901233 Calculate the square root of the right side: 1.009598991 Break this problem into two subproblems by setting (x + 0.861111111) equal to 1.009598991 and -1.009598991.Subproblem 1
x + 0.861111111 = 1.009598991 Simplifying x + 0.861111111 = 1.009598991 Reorder the terms: 0.861111111 + x = 1.009598991 Solving 0.861111111 + x = 1.009598991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.861111111' to each side of the equation. 0.861111111 + -0.861111111 + x = 1.009598991 + -0.861111111 Combine like terms: 0.861111111 + -0.861111111 = 0.000000000 0.000000000 + x = 1.009598991 + -0.861111111 x = 1.009598991 + -0.861111111 Combine like terms: 1.009598991 + -0.861111111 = 0.14848788 x = 0.14848788 Simplifying x = 0.14848788Subproblem 2
x + 0.861111111 = -1.009598991 Simplifying x + 0.861111111 = -1.009598991 Reorder the terms: 0.861111111 + x = -1.009598991 Solving 0.861111111 + x = -1.009598991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.861111111' to each side of the equation. 0.861111111 + -0.861111111 + x = -1.009598991 + -0.861111111 Combine like terms: 0.861111111 + -0.861111111 = 0.000000000 0.000000000 + x = -1.009598991 + -0.861111111 x = -1.009598991 + -0.861111111 Combine like terms: -1.009598991 + -0.861111111 = -1.870710102 x = -1.870710102 Simplifying x = -1.870710102Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.14848788, -1.870710102}Solution
x = {0.14848788, -1.870710102}
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