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Simplifying (6x2 + 3x + -5) + -1(2x2 + -7x + 8) = 0 Reorder the terms: (-5 + 3x + 6x2) + -1(2x2 + -7x + 8) = 0 Remove parenthesis around (-5 + 3x + 6x2) -5 + 3x + 6x2 + -1(2x2 + -7x + 8) = 0 Reorder the terms: -5 + 3x + 6x2 + -1(8 + -7x + 2x2) = 0 -5 + 3x + 6x2 + (8 * -1 + -7x * -1 + 2x2 * -1) = 0 -5 + 3x + 6x2 + (-8 + 7x + -2x2) = 0 Reorder the terms: -5 + -8 + 3x + 7x + 6x2 + -2x2 = 0 Combine like terms: -5 + -8 = -13 -13 + 3x + 7x + 6x2 + -2x2 = 0 Combine like terms: 3x + 7x = 10x -13 + 10x + 6x2 + -2x2 = 0 Combine like terms: 6x2 + -2x2 = 4x2 -13 + 10x + 4x2 = 0 Solving -13 + 10x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + 2.5x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 2.5x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 2.5x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 2.5x + x2 = 0 + 3.25 2.5x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 2.5x + x2 = 3.25 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 3.25 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 3.25 + 1.5625 Combine like terms: 3.25 + 1.5625 = 4.8125 1.5625 + 2.5x + x2 = 4.8125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 4.8125 Calculate the square root of the right side: 2.193741097 Break this problem into two subproblems by setting (x + 1.25) equal to 2.193741097 and -2.193741097.Subproblem 1
x + 1.25 = 2.193741097 Simplifying x + 1.25 = 2.193741097 Reorder the terms: 1.25 + x = 2.193741097 Solving 1.25 + x = 2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.193741097 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.193741097 + -1.25 x = 2.193741097 + -1.25 Combine like terms: 2.193741097 + -1.25 = 0.943741097 x = 0.943741097 Simplifying x = 0.943741097Subproblem 2
x + 1.25 = -2.193741097 Simplifying x + 1.25 = -2.193741097 Reorder the terms: 1.25 + x = -2.193741097 Solving 1.25 + x = -2.193741097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.193741097 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.193741097 + -1.25 x = -2.193741097 + -1.25 Combine like terms: -2.193741097 + -1.25 = -3.443741097 x = -3.443741097 Simplifying x = -3.443741097Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.943741097, -3.443741097}
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