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Simplifying 4x2 + -17x + 10 = 8x + 8 Reorder the terms: 10 + -17x + 4x2 = 8x + 8 Reorder the terms: 10 + -17x + 4x2 = 8 + 8x Solving 10 + -17x + 4x2 = 8 + 8x Solving for variable 'x'. Reorder the terms: 10 + -8 + -17x + -8x + 4x2 = 8 + 8x + -8 + -8x Combine like terms: 10 + -8 = 2 2 + -17x + -8x + 4x2 = 8 + 8x + -8 + -8x Combine like terms: -17x + -8x = -25x 2 + -25x + 4x2 = 8 + 8x + -8 + -8x Reorder the terms: 2 + -25x + 4x2 = 8 + -8 + 8x + -8x Combine like terms: 8 + -8 = 0 2 + -25x + 4x2 = 0 + 8x + -8x 2 + -25x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 2 + -25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -6.25x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -6.25x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -6.25x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -6.25x + x2 = 0 + -0.5 -6.25x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -6.25x + x2 = -0.5 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = -0.5 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -0.5 + 9.765625 Combine like terms: -0.5 + 9.765625 = 9.265625 9.765625 + -6.25x + x2 = 9.265625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 9.265625 Calculate the square root of the right side: 3.043948915 Break this problem into two subproblems by setting (x + -3.125) equal to 3.043948915 and -3.043948915.Subproblem 1
x + -3.125 = 3.043948915 Simplifying x + -3.125 = 3.043948915 Reorder the terms: -3.125 + x = 3.043948915 Solving -3.125 + x = 3.043948915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 3.043948915 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 3.043948915 + 3.125 x = 3.043948915 + 3.125 Combine like terms: 3.043948915 + 3.125 = 6.168948915 x = 6.168948915 Simplifying x = 6.168948915Subproblem 2
x + -3.125 = -3.043948915 Simplifying x + -3.125 = -3.043948915 Reorder the terms: -3.125 + x = -3.043948915 Solving -3.125 + x = -3.043948915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -3.043948915 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -3.043948915 + 3.125 x = -3.043948915 + 3.125 Combine like terms: -3.043948915 + 3.125 = 0.081051085 x = 0.081051085 Simplifying x = 0.081051085Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.168948915, 0.081051085}
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