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Simplifying 7 + -9x(x + 5) + -7 = 7 + 3(9 + -3x) + -81 Reorder the terms: 7 + -9x(5 + x) + -7 = 7 + 3(9 + -3x) + -81 7 + (5 * -9x + x * -9x) + -7 = 7 + 3(9 + -3x) + -81 7 + (-45x + -9x2) + -7 = 7 + 3(9 + -3x) + -81 Reorder the terms: 7 + -7 + -45x + -9x2 = 7 + 3(9 + -3x) + -81 Combine like terms: 7 + -7 = 0 0 + -45x + -9x2 = 7 + 3(9 + -3x) + -81 -45x + -9x2 = 7 + 3(9 + -3x) + -81 -45x + -9x2 = 7 + (9 * 3 + -3x * 3) + -81 -45x + -9x2 = 7 + (27 + -9x) + -81 Reorder the terms: -45x + -9x2 = 7 + 27 + -81 + -9x Combine like terms: 7 + 27 = 34 -45x + -9x2 = 34 + -81 + -9x Combine like terms: 34 + -81 = -47 -45x + -9x2 = -47 + -9x Solving -45x + -9x2 = -47 + -9x Solving for variable 'x'. Reorder the terms: 47 + -45x + 9x + -9x2 = -47 + -9x + 47 + 9x Combine like terms: -45x + 9x = -36x 47 + -36x + -9x2 = -47 + -9x + 47 + 9x Reorder the terms: 47 + -36x + -9x2 = -47 + 47 + -9x + 9x Combine like terms: -47 + 47 = 0 47 + -36x + -9x2 = 0 + -9x + 9x 47 + -36x + -9x2 = -9x + 9x Combine like terms: -9x + 9x = 0 47 + -36x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -5.222222222 + 4x + x2 = 0 Move the constant term to the right: Add '5.222222222' to each side of the equation. -5.222222222 + 4x + 5.222222222 + x2 = 0 + 5.222222222 Reorder the terms: -5.222222222 + 5.222222222 + 4x + x2 = 0 + 5.222222222 Combine like terms: -5.222222222 + 5.222222222 = 0.000000000 0.000000000 + 4x + x2 = 0 + 5.222222222 4x + x2 = 0 + 5.222222222 Combine like terms: 0 + 5.222222222 = 5.222222222 4x + x2 = 5.222222222 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 5.222222222 + 4 Reorder the terms: 4 + 4x + x2 = 5.222222222 + 4 Combine like terms: 5.222222222 + 4 = 9.222222222 4 + 4x + x2 = 9.222222222 Factor a perfect square on the left side: (x + 2)(x + 2) = 9.222222222 Calculate the square root of the right side: 3.036811193 Break this problem into two subproblems by setting (x + 2) equal to 3.036811193 and -3.036811193.Subproblem 1
x + 2 = 3.036811193 Simplifying x + 2 = 3.036811193 Reorder the terms: 2 + x = 3.036811193 Solving 2 + x = 3.036811193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.036811193 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.036811193 + -2 x = 3.036811193 + -2 Combine like terms: 3.036811193 + -2 = 1.036811193 x = 1.036811193 Simplifying x = 1.036811193Subproblem 2
x + 2 = -3.036811193 Simplifying x + 2 = -3.036811193 Reorder the terms: 2 + x = -3.036811193 Solving 2 + x = -3.036811193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.036811193 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.036811193 + -2 x = -3.036811193 + -2 Combine like terms: -3.036811193 + -2 = -5.036811193 x = -5.036811193 Simplifying x = -5.036811193Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.036811193, -5.036811193}
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