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Simplifying -4x2 + 21x + 27 = 0 Reorder the terms: 27 + 21x + -4x2 = 0 Solving 27 + 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'. -6.75 + -5.25x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + -5.25x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + -5.25x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + -5.25x + x2 = 0 + 6.75 -5.25x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 -5.25x + x2 = 6.75 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 = 6.75 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = 6.75 + 6.890625 Combine like terms: 6.75 + 6.890625 = 13.640625 6.890625 + -5.25x + x2 = 13.640625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 13.640625 Calculate the square root of the right side: 3.693321676 Break this problem into two subproblems by setting (x + -2.625) equal to 3.693321676 and -3.693321676.Subproblem 1
x + -2.625 = 3.693321676 Simplifying x + -2.625 = 3.693321676 Reorder the terms: -2.625 + x = 3.693321676 Solving -2.625 + x = 3.693321676 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 = 3.693321676 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 3.693321676 + 2.625 x = 3.693321676 + 2.625 Combine like terms: 3.693321676 + 2.625 = 6.318321676 x = 6.318321676 Simplifying x = 6.318321676Subproblem 2
x + -2.625 = -3.693321676 Simplifying x + -2.625 = -3.693321676 Reorder the terms: -2.625 + x = -3.693321676 Solving -2.625 + x = -3.693321676 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 = -3.693321676 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -3.693321676 + 2.625 x = -3.693321676 + 2.625 Combine like terms: -3.693321676 + 2.625 = -1.068321676 x = -1.068321676 Simplifying x = -1.068321676Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.318321676, -1.068321676}
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