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Simplifying (4x2 + 5x + -8) + -1(2x2 + -6x + 2) = 0 Reorder the terms: (-8 + 5x + 4x2) + -1(2x2 + -6x + 2) = 0 Remove parenthesis around (-8 + 5x + 4x2) -8 + 5x + 4x2 + -1(2x2 + -6x + 2) = 0 Reorder the terms: -8 + 5x + 4x2 + -1(2 + -6x + 2x2) = 0 -8 + 5x + 4x2 + (2 * -1 + -6x * -1 + 2x2 * -1) = 0 -8 + 5x + 4x2 + (-2 + 6x + -2x2) = 0 Reorder the terms: -8 + -2 + 5x + 6x + 4x2 + -2x2 = 0 Combine like terms: -8 + -2 = -10 -10 + 5x + 6x + 4x2 + -2x2 = 0 Combine like terms: 5x + 6x = 11x -10 + 11x + 4x2 + -2x2 = 0 Combine like terms: 4x2 + -2x2 = 2x2 -10 + 11x + 2x2 = 0 Solving -10 + 11x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + 5.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 5.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 5.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 5.5x + x2 = 0 + 5 5.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 5.5x + x2 = 5 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 5 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 5 + 7.5625 Combine like terms: 5 + 7.5625 = 12.5625 7.5625 + 5.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + 2.75) equal to 3.54436172 and -3.54436172.Subproblem 1
x + 2.75 = 3.54436172 Simplifying x + 2.75 = 3.54436172 Reorder the terms: 2.75 + x = 3.54436172 Solving 2.75 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 3.54436172 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 3.54436172 + -2.75 x = 3.54436172 + -2.75 Combine like terms: 3.54436172 + -2.75 = 0.79436172 x = 0.79436172 Simplifying x = 0.79436172Subproblem 2
x + 2.75 = -3.54436172 Simplifying x + 2.75 = -3.54436172 Reorder the terms: 2.75 + x = -3.54436172 Solving 2.75 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -3.54436172 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -3.54436172 + -2.75 x = -3.54436172 + -2.75 Combine like terms: -3.54436172 + -2.75 = -6.29436172 x = -6.29436172 Simplifying x = -6.29436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.79436172, -6.29436172}
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