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Simplifying (4x2 + x + 5) + -1(8x2 + -4x) = 0 Reorder the terms: (5 + x + 4x2) + -1(8x2 + -4x) = 0 Remove parenthesis around (5 + x + 4x2) 5 + x + 4x2 + -1(8x2 + -4x) = 0 Reorder the terms: 5 + x + 4x2 + -1(-4x + 8x2) = 0 5 + x + 4x2 + (-4x * -1 + 8x2 * -1) = 0 5 + x + 4x2 + (4x + -8x2) = 0 Reorder the terms: 5 + x + 4x + 4x2 + -8x2 = 0 Combine like terms: x + 4x = 5x 5 + 5x + 4x2 + -8x2 = 0 Combine like terms: 4x2 + -8x2 = -4x2 5 + 5x + -4x2 = 0 Solving 5 + 5x + -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'. -1.25 + -1.25x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -1.25x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -1.25x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -1.25x + x2 = 0 + 1.25 -1.25x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -1.25x + x2 = 1.25 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 1.25 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 1.25 + 0.390625 Combine like terms: 1.25 + 0.390625 = 1.640625 0.390625 + -1.25x + x2 = 1.640625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + -0.625) equal to 1.280868846 and -1.280868846.Subproblem 1
x + -0.625 = 1.280868846 Simplifying x + -0.625 = 1.280868846 Reorder the terms: -0.625 + x = 1.280868846 Solving -0.625 + x = 1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.280868846 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.280868846 + 0.625 x = 1.280868846 + 0.625 Combine like terms: 1.280868846 + 0.625 = 1.905868846 x = 1.905868846 Simplifying x = 1.905868846Subproblem 2
x + -0.625 = -1.280868846 Simplifying x + -0.625 = -1.280868846 Reorder the terms: -0.625 + x = -1.280868846 Solving -0.625 + x = -1.280868846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.280868846 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.280868846 + 0.625 x = -1.280868846 + 0.625 Combine like terms: -1.280868846 + 0.625 = -0.655868846 x = -0.655868846 Simplifying x = -0.655868846Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.905868846, -0.655868846}
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