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Simplifying 5 + -2x(2x + -3) + -1(-8 + 2x) = 0 Reorder the terms: 5 + -2x(-3 + 2x) + -1(-8 + 2x) = 0 5 + (-3 * -2x + 2x * -2x) + -1(-8 + 2x) = 0 5 + (6x + -4x2) + -1(-8 + 2x) = 0 5 + 6x + -4x2 + (-8 * -1 + 2x * -1) = 0 5 + 6x + -4x2 + (8 + -2x) = 0 Reorder the terms: 5 + 8 + 6x + -2x + -4x2 = 0 Combine like terms: 5 + 8 = 13 13 + 6x + -2x + -4x2 = 0 Combine like terms: 6x + -2x = 4x 13 + 4x + -4x2 = 0 Solving 13 + 4x + -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 + -1x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -1x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -1x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -1x + x2 = 0 + 3.25 -1x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -1x + x2 = 3.25 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 3.25 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3.25 + 0.25 Combine like terms: 3.25 + 0.25 = 3.5 0.25 + -1x + x2 = 3.5 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (x + -0.5) equal to 1.870828693 and -1.870828693.Subproblem 1
x + -0.5 = 1.870828693 Simplifying x + -0.5 = 1.870828693 Reorder the terms: -0.5 + x = 1.870828693 Solving -0.5 + x = 1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.870828693 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.870828693 + 0.5 x = 1.870828693 + 0.5 Combine like terms: 1.870828693 + 0.5 = 2.370828693 x = 2.370828693 Simplifying x = 2.370828693Subproblem 2
x + -0.5 = -1.870828693 Simplifying x + -0.5 = -1.870828693 Reorder the terms: -0.5 + x = -1.870828693 Solving -0.5 + x = -1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.870828693 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.870828693 + 0.5 x = -1.870828693 + 0.5 Combine like terms: -1.870828693 + 0.5 = -1.370828693 x = -1.370828693 Simplifying x = -1.370828693Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.370828693, -1.370828693}
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