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Simplifying (x + -4x2 + 7) + -1(5x2 + 5x + -3) = 0 Reorder the terms: (7 + x + -4x2) + -1(5x2 + 5x + -3) = 0 Remove parenthesis around (7 + x + -4x2) 7 + x + -4x2 + -1(5x2 + 5x + -3) = 0 Reorder the terms: 7 + x + -4x2 + -1(-3 + 5x + 5x2) = 0 7 + x + -4x2 + (-3 * -1 + 5x * -1 + 5x2 * -1) = 0 7 + x + -4x2 + (3 + -5x + -5x2) = 0 Reorder the terms: 7 + 3 + x + -5x + -4x2 + -5x2 = 0 Combine like terms: 7 + 3 = 10 10 + x + -5x + -4x2 + -5x2 = 0 Combine like terms: x + -5x = -4x 10 + -4x + -4x2 + -5x2 = 0 Combine like terms: -4x2 + -5x2 = -9x2 10 + -4x + -9x2 = 0 Solving 10 + -4x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1.111111111 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 0.4444444444x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 0.4444444444x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 0.4444444444x + x2 = 0 + 1.111111111 0.4444444444x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 0.4444444444x + x2 = 1.111111111 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 1.111111111 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 1.111111111 + 0.04938271604 Combine like terms: 1.111111111 + 0.04938271604 = 1.16049382704 0.04938271604 + 0.4444444444x + x2 = 1.16049382704 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 1.16049382704 Calculate the square root of the right side: 1.07726219 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 1.07726219 and -1.07726219.Subproblem 1
x + 0.2222222222 = 1.07726219 Simplifying x + 0.2222222222 = 1.07726219 Reorder the terms: 0.2222222222 + x = 1.07726219 Solving 0.2222222222 + x = 1.07726219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 1.07726219 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 1.07726219 + -0.2222222222 x = 1.07726219 + -0.2222222222 Combine like terms: 1.07726219 + -0.2222222222 = 0.8550399678 x = 0.8550399678 Simplifying x = 0.8550399678Subproblem 2
x + 0.2222222222 = -1.07726219 Simplifying x + 0.2222222222 = -1.07726219 Reorder the terms: 0.2222222222 + x = -1.07726219 Solving 0.2222222222 + x = -1.07726219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -1.07726219 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -1.07726219 + -0.2222222222 x = -1.07726219 + -0.2222222222 Combine like terms: -1.07726219 + -0.2222222222 = -1.2994844122 x = -1.2994844122 Simplifying x = -1.2994844122Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8550399678, -1.2994844122}
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