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Simplifying 4x2 + -31x + 30 = 8x + 2 Reorder the terms: 30 + -31x + 4x2 = 8x + 2 Reorder the terms: 30 + -31x + 4x2 = 2 + 8x Solving 30 + -31x + 4x2 = 2 + 8x Solving for variable 'x'. Reorder the terms: 30 + -2 + -31x + -8x + 4x2 = 2 + 8x + -2 + -8x Combine like terms: 30 + -2 = 28 28 + -31x + -8x + 4x2 = 2 + 8x + -2 + -8x Combine like terms: -31x + -8x = -39x 28 + -39x + 4x2 = 2 + 8x + -2 + -8x Reorder the terms: 28 + -39x + 4x2 = 2 + -2 + 8x + -8x Combine like terms: 2 + -2 = 0 28 + -39x + 4x2 = 0 + 8x + -8x 28 + -39x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 28 + -39x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7 + -9.75x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -9.75x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -9.75x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9.75x + x2 = 0 + -7 -9.75x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -9.75x + x2 = -7 The x term is -9.75x. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75x + 23.765625 + x2 = -7 + 23.765625 Reorder the terms: 23.765625 + -9.75x + x2 = -7 + 23.765625 Combine like terms: -7 + 23.765625 = 16.765625 23.765625 + -9.75x + x2 = 16.765625 Factor a perfect square on the left side: (x + -4.875)(x + -4.875) = 16.765625 Calculate the square root of the right side: 4.094584839 Break this problem into two subproblems by setting (x + -4.875) equal to 4.094584839 and -4.094584839.Subproblem 1
x + -4.875 = 4.094584839 Simplifying x + -4.875 = 4.094584839 Reorder the terms: -4.875 + x = 4.094584839 Solving -4.875 + x = 4.094584839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 4.094584839 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 4.094584839 + 4.875 x = 4.094584839 + 4.875 Combine like terms: 4.094584839 + 4.875 = 8.969584839 x = 8.969584839 Simplifying x = 8.969584839Subproblem 2
x + -4.875 = -4.094584839 Simplifying x + -4.875 = -4.094584839 Reorder the terms: -4.875 + x = -4.094584839 Solving -4.875 + x = -4.094584839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -4.094584839 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -4.094584839 + 4.875 x = -4.094584839 + 4.875 Combine like terms: -4.094584839 + 4.875 = 0.780415161 x = 0.780415161 Simplifying x = 0.780415161Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.969584839, 0.780415161}
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