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Simplifying (7x2 + -4x + -47) + (9x2 + 9x) = 0 Reorder the terms: (-47 + -4x + 7x2) + (9x2 + 9x) = 0 Remove parenthesis around (-47 + -4x + 7x2) -47 + -4x + 7x2 + (9x2 + 9x) = 0 Reorder the terms: -47 + -4x + 7x2 + (9x + 9x2) = 0 Remove parenthesis around (9x + 9x2) -47 + -4x + 7x2 + 9x + 9x2 = 0 Reorder the terms: -47 + -4x + 9x + 7x2 + 9x2 = 0 Combine like terms: -4x + 9x = 5x -47 + 5x + 7x2 + 9x2 = 0 Combine like terms: 7x2 + 9x2 = 16x2 -47 + 5x + 16x2 = 0 Solving -47 + 5x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.9375 + 0.3125x + x2 = 0 Move the constant term to the right: Add '2.9375' to each side of the equation. -2.9375 + 0.3125x + 2.9375 + x2 = 0 + 2.9375 Reorder the terms: -2.9375 + 2.9375 + 0.3125x + x2 = 0 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + 0.3125x + x2 = 0 + 2.9375 0.3125x + x2 = 0 + 2.9375 Combine like terms: 0 + 2.9375 = 2.9375 0.3125x + x2 = 2.9375 The x term is 0.3125x. Take half its coefficient (0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. 0.3125x + 0.0244140625 + x2 = 2.9375 + 0.0244140625 Reorder the terms: 0.0244140625 + 0.3125x + x2 = 2.9375 + 0.0244140625 Combine like terms: 2.9375 + 0.0244140625 = 2.9619140625 0.0244140625 + 0.3125x + x2 = 2.9619140625 Factor a perfect square on the left side: (x + 0.15625)(x + 0.15625) = 2.9619140625 Calculate the square root of the right side: 1.721021227 Break this problem into two subproblems by setting (x + 0.15625) equal to 1.721021227 and -1.721021227.Subproblem 1
x + 0.15625 = 1.721021227 Simplifying x + 0.15625 = 1.721021227 Reorder the terms: 0.15625 + x = 1.721021227 Solving 0.15625 + x = 1.721021227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + x = 1.721021227 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + x = 1.721021227 + -0.15625 x = 1.721021227 + -0.15625 Combine like terms: 1.721021227 + -0.15625 = 1.564771227 x = 1.564771227 Simplifying x = 1.564771227Subproblem 2
x + 0.15625 = -1.721021227 Simplifying x + 0.15625 = -1.721021227 Reorder the terms: 0.15625 + x = -1.721021227 Solving 0.15625 + x = -1.721021227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + x = -1.721021227 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + x = -1.721021227 + -0.15625 x = -1.721021227 + -0.15625 Combine like terms: -1.721021227 + -0.15625 = -1.877271227 x = -1.877271227 Simplifying x = -1.877271227Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.564771227, -1.877271227}
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