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Simplifying 7x2 + 14x + -64 = 3 Reorder the terms: -64 + 14x + 7x2 = 3 Solving -64 + 14x + 7x2 = 3 Solving for variable 'x'. Reorder the terms: -64 + -3 + 14x + 7x2 = 3 + -3 Combine like terms: -64 + -3 = -67 -67 + 14x + 7x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -67 + 14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -9.571428571 + 2x + x2 = 0 Move the constant term to the right: Add '9.571428571' to each side of the equation. -9.571428571 + 2x + 9.571428571 + x2 = 0 + 9.571428571 Reorder the terms: -9.571428571 + 9.571428571 + 2x + x2 = 0 + 9.571428571 Combine like terms: -9.571428571 + 9.571428571 = 0.000000000 0.000000000 + 2x + x2 = 0 + 9.571428571 2x + x2 = 0 + 9.571428571 Combine like terms: 0 + 9.571428571 = 9.571428571 2x + x2 = 9.571428571 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 9.571428571 + 1 Reorder the terms: 1 + 2x + x2 = 9.571428571 + 1 Combine like terms: 9.571428571 + 1 = 10.571428571 1 + 2x + x2 = 10.571428571 Factor a perfect square on the left side: (x + 1)(x + 1) = 10.571428571 Calculate the square root of the right side: 3.251373336 Break this problem into two subproblems by setting (x + 1) equal to 3.251373336 and -3.251373336.Subproblem 1
x + 1 = 3.251373336 Simplifying x + 1 = 3.251373336 Reorder the terms: 1 + x = 3.251373336 Solving 1 + x = 3.251373336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.251373336 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.251373336 + -1 x = 3.251373336 + -1 Combine like terms: 3.251373336 + -1 = 2.251373336 x = 2.251373336 Simplifying x = 2.251373336Subproblem 2
x + 1 = -3.251373336 Simplifying x + 1 = -3.251373336 Reorder the terms: 1 + x = -3.251373336 Solving 1 + x = -3.251373336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.251373336 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.251373336 + -1 x = -3.251373336 + -1 Combine like terms: -3.251373336 + -1 = -4.251373336 x = -4.251373336 Simplifying x = -4.251373336Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.251373336, -4.251373336}
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