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Simplifying 4x2 + -7x + -21 = 0 Reorder the terms: -21 + -7x + 4x2 = 0 Solving -21 + -7x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + -1.75x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -1.75x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -1.75x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -1.75x + x2 = 0 + 5.25 -1.75x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -1.75x + x2 = 5.25 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 = 5.25 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 5.25 + 0.765625 Combine like terms: 5.25 + 0.765625 = 6.015625 0.765625 + -1.75x + x2 = 6.015625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (x + -0.875) equal to 2.452677109 and -2.452677109.Subproblem 1
x + -0.875 = 2.452677109 Simplifying x + -0.875 = 2.452677109 Reorder the terms: -0.875 + x = 2.452677109 Solving -0.875 + x = 2.452677109 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 = 2.452677109 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 2.452677109 + 0.875 x = 2.452677109 + 0.875 Combine like terms: 2.452677109 + 0.875 = 3.327677109 x = 3.327677109 Simplifying x = 3.327677109Subproblem 2
x + -0.875 = -2.452677109 Simplifying x + -0.875 = -2.452677109 Reorder the terms: -0.875 + x = -2.452677109 Solving -0.875 + x = -2.452677109 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 = -2.452677109 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -2.452677109 + 0.875 x = -2.452677109 + 0.875 Combine like terms: -2.452677109 + 0.875 = -1.577677109 x = -1.577677109 Simplifying x = -1.577677109Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.327677109, -1.577677109}
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