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Simplifying -4x2 + 21x + 20 = 0 Reorder the terms: 20 + 21x + -4x2 = 0 Solving 20 + 21x + -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 + -5.25x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -5.25x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -5.25x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -5.25x + x2 = 0 + 5 -5.25x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -5.25x + x2 = 5 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = 5 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = 5 + 6.890625 Combine like terms: 5 + 6.890625 = 11.890625 6.890625 + -5.25x + x2 = 11.890625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 11.890625 Calculate the square root of the right side: 3.448278556 Break this problem into two subproblems by setting (x + -2.625) equal to 3.448278556 and -3.448278556.Subproblem 1
x + -2.625 = 3.448278556 Simplifying x + -2.625 = 3.448278556 Reorder the terms: -2.625 + x = 3.448278556 Solving -2.625 + x = 3.448278556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 3.448278556 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 3.448278556 + 2.625 x = 3.448278556 + 2.625 Combine like terms: 3.448278556 + 2.625 = 6.073278556 x = 6.073278556 Simplifying x = 6.073278556Subproblem 2
x + -2.625 = -3.448278556 Simplifying x + -2.625 = -3.448278556 Reorder the terms: -2.625 + x = -3.448278556 Solving -2.625 + x = -3.448278556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -3.448278556 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -3.448278556 + 2.625 x = -3.448278556 + 2.625 Combine like terms: -3.448278556 + 2.625 = -0.823278556 x = -0.823278556 Simplifying x = -0.823278556Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.073278556, -0.823278556}
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