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Simplifying 81x2 + 72x + 16 = 10 Reorder the terms: 16 + 72x + 81x2 = 10 Solving 16 + 72x + 81x2 = 10 Solving for variable 'x'. Reorder the terms: 16 + -10 + 72x + 81x2 = 10 + -10 Combine like terms: 16 + -10 = 6 6 + 72x + 81x2 = 10 + -10 Combine like terms: 10 + -10 = 0 6 + 72x + 81x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(2 + 24x + 27x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + 24x + 27x2)' equal to zero and attempt to solve: Simplifying 2 + 24x + 27x2 = 0 Solving 2 + 24x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 0.07407407407 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '-0.07407407407' to each side of the equation. 0.07407407407 + 0.8888888889x + -0.07407407407 + x2 = 0 + -0.07407407407 Reorder the terms: 0.07407407407 + -0.07407407407 + 0.8888888889x + x2 = 0 + -0.07407407407 Combine like terms: 0.07407407407 + -0.07407407407 = 0.00000000000 0.00000000000 + 0.8888888889x + x2 = 0 + -0.07407407407 0.8888888889x + x2 = 0 + -0.07407407407 Combine like terms: 0 + -0.07407407407 = -0.07407407407 0.8888888889x + x2 = -0.07407407407 The x term is 0.8888888889x. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x + 0.1975308642 + x2 = -0.07407407407 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = -0.07407407407 + 0.1975308642 Combine like terms: -0.07407407407 + 0.1975308642 = 0.12345679013 0.1975308642 + 0.8888888889x + x2 = 0.12345679013 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 0.12345679013 Calculate the square root of the right side: 0.351364184 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 0.351364184 and -0.351364184.Subproblem 1
x + 0.4444444445 = 0.351364184 Simplifying x + 0.4444444445 = 0.351364184 Reorder the terms: 0.4444444445 + x = 0.351364184 Solving 0.4444444445 + x = 0.351364184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 0.351364184 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 0.351364184 + -0.4444444445 x = 0.351364184 + -0.4444444445 Combine like terms: 0.351364184 + -0.4444444445 = -0.0930802605 x = -0.0930802605 Simplifying x = -0.0930802605Subproblem 2
x + 0.4444444445 = -0.351364184 Simplifying x + 0.4444444445 = -0.351364184 Reorder the terms: 0.4444444445 + x = -0.351364184 Solving 0.4444444445 + x = -0.351364184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -0.351364184 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -0.351364184 + -0.4444444445 x = -0.351364184 + -0.4444444445 Combine like terms: -0.351364184 + -0.4444444445 = -0.7958086285 x = -0.7958086285 Simplifying x = -0.7958086285Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0930802605, -0.7958086285}Solution
x = {-0.0930802605, -0.7958086285}
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