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Simplifying (4x2 + 3x + 5) + -1(6x2 + -8) = 0 Reorder the terms: (5 + 3x + 4x2) + -1(6x2 + -8) = 0 Remove parenthesis around (5 + 3x + 4x2) 5 + 3x + 4x2 + -1(6x2 + -8) = 0 Reorder the terms: 5 + 3x + 4x2 + -1(-8 + 6x2) = 0 5 + 3x + 4x2 + (-8 * -1 + 6x2 * -1) = 0 5 + 3x + 4x2 + (8 + -6x2) = 0 Reorder the terms: 5 + 8 + 3x + 4x2 + -6x2 = 0 Combine like terms: 5 + 8 = 13 13 + 3x + 4x2 + -6x2 = 0 Combine like terms: 4x2 + -6x2 = -2x2 13 + 3x + -2x2 = 0 Solving 13 + 3x + -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'. -6.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -1.5x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -1.5x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -1.5x + x2 = 0 + 6.5 -1.5x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -1.5x + x2 = 6.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 6.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 6.5 + 0.5625 Combine like terms: 6.5 + 0.5625 = 7.0625 0.5625 + -1.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + -0.75) equal to 2.657536453 and -2.657536453.Subproblem 1
x + -0.75 = 2.657536453 Simplifying x + -0.75 = 2.657536453 Reorder the terms: -0.75 + x = 2.657536453 Solving -0.75 + x = 2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.657536453 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.657536453 + 0.75 x = 2.657536453 + 0.75 Combine like terms: 2.657536453 + 0.75 = 3.407536453 x = 3.407536453 Simplifying x = 3.407536453Subproblem 2
x + -0.75 = -2.657536453 Simplifying x + -0.75 = -2.657536453 Reorder the terms: -0.75 + x = -2.657536453 Solving -0.75 + x = -2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.657536453 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.657536453 + 0.75 x = -2.657536453 + 0.75 Combine like terms: -2.657536453 + 0.75 = -1.907536453 x = -1.907536453 Simplifying x = -1.907536453Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.407536453, -1.907536453}
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