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Simplifying 5x(2x + -1) = 25 + 3(x + -3) Reorder the terms: 5x(-1 + 2x) = 25 + 3(x + -3) (-1 * 5x + 2x * 5x) = 25 + 3(x + -3) (-5x + 10x2) = 25 + 3(x + -3) Reorder the terms: -5x + 10x2 = 25 + 3(-3 + x) -5x + 10x2 = 25 + (-3 * 3 + x * 3) -5x + 10x2 = 25 + (-9 + 3x) Combine like terms: 25 + -9 = 16 -5x + 10x2 = 16 + 3x Solving -5x + 10x2 = 16 + 3x Solving for variable 'x'. Reorder the terms: -16 + -5x + -3x + 10x2 = 16 + 3x + -16 + -3x Combine like terms: -5x + -3x = -8x -16 + -8x + 10x2 = 16 + 3x + -16 + -3x Reorder the terms: -16 + -8x + 10x2 = 16 + -16 + 3x + -3x Combine like terms: 16 + -16 = 0 -16 + -8x + 10x2 = 0 + 3x + -3x -16 + -8x + 10x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -16 + -8x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -4x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -4x + 5x2)' equal to zero and attempt to solve: Simplifying -8 + -4x + 5x2 = 0 Solving -8 + -4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + -0.8x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -0.8x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -0.8x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -0.8x + x2 = 0 + 1.6 -0.8x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -0.8x + x2 = 1.6 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 1.6 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 1.6 + 0.16 Combine like terms: 1.6 + 0.16 = 1.76 0.16 + -0.8x + x2 = 1.76 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (x + -0.4) equal to 1.326649916 and -1.326649916.Subproblem 1
x + -0.4 = 1.326649916 Simplifying x + -0.4 = 1.326649916 Reorder the terms: -0.4 + x = 1.326649916 Solving -0.4 + x = 1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.326649916 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.326649916 + 0.4 x = 1.326649916 + 0.4 Combine like terms: 1.326649916 + 0.4 = 1.726649916 x = 1.726649916 Simplifying x = 1.726649916Subproblem 2
x + -0.4 = -1.326649916 Simplifying x + -0.4 = -1.326649916 Reorder the terms: -0.4 + x = -1.326649916 Solving -0.4 + x = -1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.326649916 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.326649916 + 0.4 x = -1.326649916 + 0.4 Combine like terms: -1.326649916 + 0.4 = -0.926649916 x = -0.926649916 Simplifying x = -0.926649916Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.726649916, -0.926649916}Solution
x = {1.726649916, -0.926649916}
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