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Simplifying 4x2 + -13x + 21 = 8x + 11 Reorder the terms: 21 + -13x + 4x2 = 8x + 11 Reorder the terms: 21 + -13x + 4x2 = 11 + 8x Solving 21 + -13x + 4x2 = 11 + 8x Solving for variable 'x'. Reorder the terms: 21 + -11 + -13x + -8x + 4x2 = 11 + 8x + -11 + -8x Combine like terms: 21 + -11 = 10 10 + -13x + -8x + 4x2 = 11 + 8x + -11 + -8x Combine like terms: -13x + -8x = -21x 10 + -21x + 4x2 = 11 + 8x + -11 + -8x Reorder the terms: 10 + -21x + 4x2 = 11 + -11 + 8x + -8x Combine like terms: 11 + -11 = 0 10 + -21x + 4x2 = 0 + 8x + -8x 10 + -21x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 10 + -21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.5 + -5.25x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -5.25x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -5.25x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -5.25x + x2 = 0 + -2.5 -5.25x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -5.25x + x2 = -2.5 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 = -2.5 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -2.5 + 6.890625 Combine like terms: -2.5 + 6.890625 = 4.390625 6.890625 + -5.25x + x2 = 4.390625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (x + -2.625) equal to 2.095381827 and -2.095381827.Subproblem 1
x + -2.625 = 2.095381827 Simplifying x + -2.625 = 2.095381827 Reorder the terms: -2.625 + x = 2.095381827 Solving -2.625 + x = 2.095381827 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 = 2.095381827 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 2.095381827 + 2.625 x = 2.095381827 + 2.625 Combine like terms: 2.095381827 + 2.625 = 4.720381827 x = 4.720381827 Simplifying x = 4.720381827Subproblem 2
x + -2.625 = -2.095381827 Simplifying x + -2.625 = -2.095381827 Reorder the terms: -2.625 + x = -2.095381827 Solving -2.625 + x = -2.095381827 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 = -2.095381827 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -2.095381827 + 2.625 x = -2.095381827 + 2.625 Combine like terms: -2.095381827 + 2.625 = 0.529618173 x = 0.529618173 Simplifying x = 0.529618173Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.720381827, 0.529618173}
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