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Simplifying 3x2 + -12x + 13 = 4x2 + 20x + 5 Reorder the terms: 13 + -12x + 3x2 = 4x2 + 20x + 5 Reorder the terms: 13 + -12x + 3x2 = 5 + 20x + 4x2 Solving 13 + -12x + 3x2 = 5 + 20x + 4x2 Solving for variable 'x'. Reorder the terms: 13 + -5 + -12x + -20x + 3x2 + -4x2 = 5 + 20x + 4x2 + -5 + -20x + -4x2 Combine like terms: 13 + -5 = 8 8 + -12x + -20x + 3x2 + -4x2 = 5 + 20x + 4x2 + -5 + -20x + -4x2 Combine like terms: -12x + -20x = -32x 8 + -32x + 3x2 + -4x2 = 5 + 20x + 4x2 + -5 + -20x + -4x2 Combine like terms: 3x2 + -4x2 = -1x2 8 + -32x + -1x2 = 5 + 20x + 4x2 + -5 + -20x + -4x2 Reorder the terms: 8 + -32x + -1x2 = 5 + -5 + 20x + -20x + 4x2 + -4x2 Combine like terms: 5 + -5 = 0 8 + -32x + -1x2 = 0 + 20x + -20x + 4x2 + -4x2 8 + -32x + -1x2 = 20x + -20x + 4x2 + -4x2 Combine like terms: 20x + -20x = 0 8 + -32x + -1x2 = 0 + 4x2 + -4x2 8 + -32x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 8 + -32x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + 32x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 32x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 32x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 32x + x2 = 0 + 8 32x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 32x + x2 = 8 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 8 + 256 Reorder the terms: 256 + 32x + x2 = 8 + 256 Combine like terms: 8 + 256 = 264 256 + 32x + x2 = 264 Factor a perfect square on the left side: (x + 16)(x + 16) = 264 Calculate the square root of the right side: 16.248076809 Break this problem into two subproblems by setting (x + 16) equal to 16.248076809 and -16.248076809.Subproblem 1
x + 16 = 16.248076809 Simplifying x + 16 = 16.248076809 Reorder the terms: 16 + x = 16.248076809 Solving 16 + x = 16.248076809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 16.248076809 + -16 Combine like terms: 16 + -16 = 0 0 + x = 16.248076809 + -16 x = 16.248076809 + -16 Combine like terms: 16.248076809 + -16 = 0.248076809 x = 0.248076809 Simplifying x = 0.248076809Subproblem 2
x + 16 = -16.248076809 Simplifying x + 16 = -16.248076809 Reorder the terms: 16 + x = -16.248076809 Solving 16 + x = -16.248076809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -16.248076809 + -16 Combine like terms: 16 + -16 = 0 0 + x = -16.248076809 + -16 x = -16.248076809 + -16 Combine like terms: -16.248076809 + -16 = -32.248076809 x = -32.248076809 Simplifying x = -32.248076809Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.248076809, -32.248076809}
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