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Simplifying 4x2 + -13 = 7x + 20 Reorder the terms: -13 + 4x2 = 7x + 20 Reorder the terms: -13 + 4x2 = 20 + 7x Solving -13 + 4x2 = 20 + 7x Solving for variable 'x'. Reorder the terms: -13 + -20 + -7x + 4x2 = 20 + 7x + -20 + -7x Combine like terms: -13 + -20 = -33 -33 + -7x + 4x2 = 20 + 7x + -20 + -7x Reorder the terms: -33 + -7x + 4x2 = 20 + -20 + 7x + -7x Combine like terms: 20 + -20 = 0 -33 + -7x + 4x2 = 0 + 7x + -7x -33 + -7x + 4x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -33 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.25 + -1.75x + x2 = 0 Move the constant term to the right: Add '8.25' to each side of the equation. -8.25 + -1.75x + 8.25 + x2 = 0 + 8.25 Reorder the terms: -8.25 + 8.25 + -1.75x + x2 = 0 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + -1.75x + x2 = 0 + 8.25 -1.75x + x2 = 0 + 8.25 Combine like terms: 0 + 8.25 = 8.25 -1.75x + x2 = 8.25 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 8.25 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 8.25 + 0.765625 Combine like terms: 8.25 + 0.765625 = 9.015625 0.765625 + -1.75x + x2 = 9.015625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 9.015625 Calculate the square root of the right side: 3.002603037 Break this problem into two subproblems by setting (x + -0.875) equal to 3.002603037 and -3.002603037.Subproblem 1
x + -0.875 = 3.002603037 Simplifying x + -0.875 = 3.002603037 Reorder the terms: -0.875 + x = 3.002603037 Solving -0.875 + x = 3.002603037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 3.002603037 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 3.002603037 + 0.875 x = 3.002603037 + 0.875 Combine like terms: 3.002603037 + 0.875 = 3.877603037 x = 3.877603037 Simplifying x = 3.877603037Subproblem 2
x + -0.875 = -3.002603037 Simplifying x + -0.875 = -3.002603037 Reorder the terms: -0.875 + x = -3.002603037 Solving -0.875 + x = -3.002603037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -3.002603037 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -3.002603037 + 0.875 x = -3.002603037 + 0.875 Combine like terms: -3.002603037 + 0.875 = -2.127603037 x = -2.127603037 Simplifying x = -2.127603037Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.877603037, -2.127603037}
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