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Simplifying 987 + 2x(4x + -5) = 6x + 2921 Reorder the terms: 987 + 2x(-5 + 4x) = 6x + 2921 987 + (-5 * 2x + 4x * 2x) = 6x + 2921 987 + (-10x + 8x2) = 6x + 2921 Reorder the terms: 987 + -10x + 8x2 = 2921 + 6x Solving 987 + -10x + 8x2 = 2921 + 6x Solving for variable 'x'. Reorder the terms: 987 + -2921 + -10x + -6x + 8x2 = 2921 + 6x + -2921 + -6x Combine like terms: 987 + -2921 = -1934 -1934 + -10x + -6x + 8x2 = 2921 + 6x + -2921 + -6x Combine like terms: -10x + -6x = -16x -1934 + -16x + 8x2 = 2921 + 6x + -2921 + -6x Reorder the terms: -1934 + -16x + 8x2 = 2921 + -2921 + 6x + -6x Combine like terms: 2921 + -2921 = 0 -1934 + -16x + 8x2 = 0 + 6x + -6x -1934 + -16x + 8x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -1934 + -16x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-967 + -8x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-967 + -8x + 4x2)' equal to zero and attempt to solve: Simplifying -967 + -8x + 4x2 = 0 Solving -967 + -8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -241.75 + -2x + x2 = 0 Move the constant term to the right: Add '241.75' to each side of the equation. -241.75 + -2x + 241.75 + x2 = 0 + 241.75 Reorder the terms: -241.75 + 241.75 + -2x + x2 = 0 + 241.75 Combine like terms: -241.75 + 241.75 = 0.00 0.00 + -2x + x2 = 0 + 241.75 -2x + x2 = 0 + 241.75 Combine like terms: 0 + 241.75 = 241.75 -2x + x2 = 241.75 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 241.75 + 1 Reorder the terms: 1 + -2x + x2 = 241.75 + 1 Combine like terms: 241.75 + 1 = 242.75 1 + -2x + x2 = 242.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 242.75 Calculate the square root of the right side: 15.580436451 Break this problem into two subproblems by setting (x + -1) equal to 15.580436451 and -15.580436451.Subproblem 1
x + -1 = 15.580436451 Simplifying x + -1 = 15.580436451 Reorder the terms: -1 + x = 15.580436451 Solving -1 + x = 15.580436451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 15.580436451 + 1 Combine like terms: -1 + 1 = 0 0 + x = 15.580436451 + 1 x = 15.580436451 + 1 Combine like terms: 15.580436451 + 1 = 16.580436451 x = 16.580436451 Simplifying x = 16.580436451Subproblem 2
x + -1 = -15.580436451 Simplifying x + -1 = -15.580436451 Reorder the terms: -1 + x = -15.580436451 Solving -1 + x = -15.580436451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -15.580436451 + 1 Combine like terms: -1 + 1 = 0 0 + x = -15.580436451 + 1 x = -15.580436451 + 1 Combine like terms: -15.580436451 + 1 = -14.580436451 x = -14.580436451 Simplifying x = -14.580436451Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.580436451, -14.580436451}Solution
x = {16.580436451, -14.580436451}
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