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Simplifying 81x2 + 72x + 16 + -1(9x + -4)(3x + -5) = 0 Reorder the terms: 81x2 + 72x + 16 + -1(-4 + 9x)(3x + -5) = 0 Reorder the terms: 81x2 + 72x + 16 + -1(-4 + 9x)(-5 + 3x) = 0 Multiply (-4 + 9x) * (-5 + 3x) 81x2 + 72x + 16 + -1(-4(-5 + 3x) + 9x * (-5 + 3x)) = 0 81x2 + 72x + 16 + -1((-5 * -4 + 3x * -4) + 9x * (-5 + 3x)) = 0 81x2 + 72x + 16 + -1((20 + -12x) + 9x * (-5 + 3x)) = 0 81x2 + 72x + 16 + -1(20 + -12x + (-5 * 9x + 3x * 9x)) = 0 81x2 + 72x + 16 + -1(20 + -12x + (-45x + 27x2)) = 0 Combine like terms: -12x + -45x = -57x 81x2 + 72x + 16 + -1(20 + -57x + 27x2) = 0 81x2 + 72x + 16 + (20 * -1 + -57x * -1 + 27x2 * -1) = 0 81x2 + 72x + 16 + (-20 + 57x + -27x2) = 0 Reorder the terms: 16 + -20 + 72x + 57x + 81x2 + -27x2 = 0 Combine like terms: 16 + -20 = -4 -4 + 72x + 57x + 81x2 + -27x2 = 0 Combine like terms: 72x + 57x = 129x -4 + 129x + 81x2 + -27x2 = 0 Combine like terms: 81x2 + -27x2 = 54x2 -4 + 129x + 54x2 = 0 Solving -4 + 129x + 54x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. -0.07407407407 + 2.388888889x + x2 = 0 Move the constant term to the right: Add '0.07407407407' to each side of the equation. -0.07407407407 + 2.388888889x + 0.07407407407 + x2 = 0 + 0.07407407407 Reorder the terms: -0.07407407407 + 0.07407407407 + 2.388888889x + x2 = 0 + 0.07407407407 Combine like terms: -0.07407407407 + 0.07407407407 = 0.00000000000 0.00000000000 + 2.388888889x + x2 = 0 + 0.07407407407 2.388888889x + x2 = 0 + 0.07407407407 Combine like terms: 0 + 0.07407407407 = 0.07407407407 2.388888889x + x2 = 0.07407407407 The x term is 2.388888889x. Take half its coefficient (1.194444445). Square it (1.426697532) and add it to both sides. Add '1.426697532' to each side of the equation. 2.388888889x + 1.426697532 + x2 = 0.07407407407 + 1.426697532 Reorder the terms: 1.426697532 + 2.388888889x + x2 = 0.07407407407 + 1.426697532 Combine like terms: 0.07407407407 + 1.426697532 = 1.50077160607 1.426697532 + 2.388888889x + x2 = 1.50077160607 Factor a perfect square on the left side: (x + 1.194444445)(x + 1.194444445) = 1.50077160607 Calculate the square root of the right side: 1.225059838 Break this problem into two subproblems by setting (x + 1.194444445) equal to 1.225059838 and -1.225059838.Subproblem 1
x + 1.194444445 = 1.225059838 Simplifying x + 1.194444445 = 1.225059838 Reorder the terms: 1.194444445 + x = 1.225059838 Solving 1.194444445 + x = 1.225059838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.194444445' to each side of the equation. 1.194444445 + -1.194444445 + x = 1.225059838 + -1.194444445 Combine like terms: 1.194444445 + -1.194444445 = 0.000000000 0.000000000 + x = 1.225059838 + -1.194444445 x = 1.225059838 + -1.194444445 Combine like terms: 1.225059838 + -1.194444445 = 0.030615393 x = 0.030615393 Simplifying x = 0.030615393Subproblem 2
x + 1.194444445 = -1.225059838 Simplifying x + 1.194444445 = -1.225059838 Reorder the terms: 1.194444445 + x = -1.225059838 Solving 1.194444445 + x = -1.225059838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.194444445' to each side of the equation. 1.194444445 + -1.194444445 + x = -1.225059838 + -1.194444445 Combine like terms: 1.194444445 + -1.194444445 = 0.000000000 0.000000000 + x = -1.225059838 + -1.194444445 x = -1.225059838 + -1.194444445 Combine like terms: -1.225059838 + -1.194444445 = -2.419504283 x = -2.419504283 Simplifying x = -2.419504283Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.030615393, -2.419504283}
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