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Simplifying 8x2 = 46x + 30 Reorder the terms: 8x2 = 30 + 46x Solving 8x2 = 30 + 46x Solving for variable 'x'. Reorder the terms: -30 + -46x + 8x2 = 30 + 46x + -30 + -46x Reorder the terms: -30 + -46x + 8x2 = 30 + -30 + 46x + -46x Combine like terms: 30 + -30 = 0 -30 + -46x + 8x2 = 0 + 46x + -46x -30 + -46x + 8x2 = 46x + -46x Combine like terms: 46x + -46x = 0 -30 + -46x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -23x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -23x + 4x2)' equal to zero and attempt to solve: Simplifying -15 + -23x + 4x2 = 0 Solving -15 + -23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -5.75x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -5.75x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -5.75x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -5.75x + x2 = 0 + 3.75 -5.75x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -5.75x + x2 = 3.75 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = 3.75 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = 3.75 + 8.265625 Combine like terms: 3.75 + 8.265625 = 12.015625 8.265625 + -5.75x + x2 = 12.015625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 12.015625 Calculate the square root of the right side: 3.466356156 Break this problem into two subproblems by setting (x + -2.875) equal to 3.466356156 and -3.466356156.Subproblem 1
x + -2.875 = 3.466356156 Simplifying x + -2.875 = 3.466356156 Reorder the terms: -2.875 + x = 3.466356156 Solving -2.875 + x = 3.466356156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 3.466356156 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 3.466356156 + 2.875 x = 3.466356156 + 2.875 Combine like terms: 3.466356156 + 2.875 = 6.341356156 x = 6.341356156 Simplifying x = 6.341356156Subproblem 2
x + -2.875 = -3.466356156 Simplifying x + -2.875 = -3.466356156 Reorder the terms: -2.875 + x = -3.466356156 Solving -2.875 + x = -3.466356156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -3.466356156 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -3.466356156 + 2.875 x = -3.466356156 + 2.875 Combine like terms: -3.466356156 + 2.875 = -0.591356156 x = -0.591356156 Simplifying x = -0.591356156Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.341356156, -0.591356156}Solution
x = {6.341356156, -0.591356156}
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