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Simplifying 7x(2x + 8) + -4(2x + -9) = 0 Reorder the terms: 7x(8 + 2x) + -4(2x + -9) = 0 (8 * 7x + 2x * 7x) + -4(2x + -9) = 0 (56x + 14x2) + -4(2x + -9) = 0 Reorder the terms: 56x + 14x2 + -4(-9 + 2x) = 0 56x + 14x2 + (-9 * -4 + 2x * -4) = 0 56x + 14x2 + (36 + -8x) = 0 Reorder the terms: 36 + 56x + -8x + 14x2 = 0 Combine like terms: 56x + -8x = 48x 36 + 48x + 14x2 = 0 Solving 36 + 48x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(18 + 24x + 7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + 24x + 7x2)' equal to zero and attempt to solve: Simplifying 18 + 24x + 7x2 = 0 Solving 18 + 24x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.571428571 + 3.428571429x + x2 = 0 Move the constant term to the right: Add '-2.571428571' to each side of the equation. 2.571428571 + 3.428571429x + -2.571428571 + x2 = 0 + -2.571428571 Reorder the terms: 2.571428571 + -2.571428571 + 3.428571429x + x2 = 0 + -2.571428571 Combine like terms: 2.571428571 + -2.571428571 = 0.000000000 0.000000000 + 3.428571429x + x2 = 0 + -2.571428571 3.428571429x + x2 = 0 + -2.571428571 Combine like terms: 0 + -2.571428571 = -2.571428571 3.428571429x + x2 = -2.571428571 The x term is 3.428571429x. Take half its coefficient (1.714285715). Square it (2.938775513) and add it to both sides. Add '2.938775513' to each side of the equation. 3.428571429x + 2.938775513 + x2 = -2.571428571 + 2.938775513 Reorder the terms: 2.938775513 + 3.428571429x + x2 = -2.571428571 + 2.938775513 Combine like terms: -2.571428571 + 2.938775513 = 0.367346942 2.938775513 + 3.428571429x + x2 = 0.367346942 Factor a perfect square on the left side: (x + 1.714285715)(x + 1.714285715) = 0.367346942 Calculate the square root of the right side: 0.606091529 Break this problem into two subproblems by setting (x + 1.714285715) equal to 0.606091529 and -0.606091529.Subproblem 1
x + 1.714285715 = 0.606091529 Simplifying x + 1.714285715 = 0.606091529 Reorder the terms: 1.714285715 + x = 0.606091529 Solving 1.714285715 + x = 0.606091529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.714285715' to each side of the equation. 1.714285715 + -1.714285715 + x = 0.606091529 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = 0.606091529 + -1.714285715 x = 0.606091529 + -1.714285715 Combine like terms: 0.606091529 + -1.714285715 = -1.108194186 x = -1.108194186 Simplifying x = -1.108194186Subproblem 2
x + 1.714285715 = -0.606091529 Simplifying x + 1.714285715 = -0.606091529 Reorder the terms: 1.714285715 + x = -0.606091529 Solving 1.714285715 + x = -0.606091529 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.714285715' to each side of the equation. 1.714285715 + -1.714285715 + x = -0.606091529 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = -0.606091529 + -1.714285715 x = -0.606091529 + -1.714285715 Combine like terms: -0.606091529 + -1.714285715 = -2.320377244 x = -2.320377244 Simplifying x = -2.320377244Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.108194186, -2.320377244}Solution
x = {-1.108194186, -2.320377244}
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